Devore-Probability&Statistics for Engineering 9/e

1. 6/7 points | Previous Answers DevoreStat9 2.R.003. My Notes

Suppose we have 14 items that we will randomly place into 6 bins, each with equal probability. Determine the probability that we will do this in such a way that no bin is empty.

Find the solution analytically. You might find it easiest to think of the problem in terms of six events

A_i,

i = 1,

…, 6, where

A_i

represents the event that bin i is empty, and calculate

P(A₁^C ∩

∩ A₆^C).

The analytic solution may be easiest to do using DeMorgan's laws, which state that

(A ∪ B)^C = A^C ∩ B^C

and

(A ∩ B)^C = A^C ∪ B^C.

(Round your answer to four decimal places.)

Next, we will determine the probability that no bin is empty by simulating the experiment many times.

Fill in the missing pieces of the R code below that can be used to run the simulation. (Simulate the experiment 10,000 times. Enter your answers as integers.)

nrep =

res = numeric(nrep)

for (i in 1:nrep){

bins = sample

1:6,

, replace =

res[i] =

length(table(bins)) ==

}

mean

Report the estimated probability obtained from simulating the previously described experiment 10,000 times. (Round your answer to four decimal places.)

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2. 0/9 points | Previous Answers DevoreStat9 6.R.002. My Notes

3. 1/4 points | Previous Answers DevoreStat9 7.R.002. My Notes

Use R to answer the following question.

The alternating current (AC) breakdown voltage of an insulating liquid indicates its dielectric strength. An article gave the following data on breakdown voltage (kV) of a particular circuit under certain conditions.

60,
50,
53,
57,
41,
53,
55,
60,
59,
64,
50,
53,
64,
62,
50,
67,
54,
55,
57,
50,
55,
50,
56,
55,
46,
55,
53,
54,
52,
47,
48,
55,
57,
48,
61,
57,
59,
55,
53,
57,
53,
52,
50,
55,
60,
50,
56,
58

Imagine that manufacturers will only consider the production of these circuits successful if the average breakdown voltage is greater than 53 kV.

Calculate a 99% lower confidence bound for average breakdown voltage (in kV). (Round your answer to three decimal places.)

kV

Can they be 99% confident that the above criterion has been met? Answer the question by interpreting the 99% lower confidence bound calculated above.

Manufacturers cannot be 99% confident that the population mean average breakdown voltage is greater than 53 kV since the 99% lower confidence bound is less than 53 kV. Manufacturers cannot be 99% confident that the population mean average breakdown voltage is greater than 53 kV since the 99% lower confidence bound is greater than 53 kV. Manufacturers can be 99% confident that the population mean average breakdown voltage is greater than 53 kV since the 99% lower confidence bound is greater than 53 kV. Manufacturers can be 99% confident that the population mean average breakdown voltage is greater than 53 kV since the 99% lower confidence bound is less than 53 kV.

Calculate a 95% lower confidence bound for the average breakdown voltage (in kV). (Round your answer to three decimal places.)

kV

Can they be 95% confident that the above criterion has been met? Answer the question by interpreting the 95% lower confidence bound calculated above.

Manufacturers cannot be 95% confident that the population mean average breakdown voltage is greater than 53 kV since the 95% lower confidence bound is less than 53 kV. Manufacturers cannot be 95% confident that the population mean average breakdown voltage is greater than 53 kV since the 95% lower confidence bound is greater than 53 kV. Manufacturers can be 95% confident that the population mean average breakdown voltage is greater than 53 kV since the 95% lower confidence bound is greater than 53 kV. Manufacturers can be 95% confident that the population mean average breakdown voltage is greater than 53 kV since the 95% lower confidence bound is less than 53 kV.

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4. 1/54 points | Previous Answers DevoreStat9 1.R.001.Lab. My Notes

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The data are available in a csv linked to below, and report on the 9-month salaries of professors at a specific college in the United States during a particular academic year. The data documentation states that this data was specifically meant to help the administration monitor any gender-based discrepancies in salary. There were six variables recorded in this dataset, namely "rank," "discipline," "yrs.since.phd," "yrs.service," "sex," and "salary." The "rank" variable has values of AsstProf, AssocProf, and Prof to denote the three levels for tenure-track faculty members as either assistant (lowest level), associate (intermediate level), or full professors. The "discipline" variable takes the values A and B, to denote more theoretical vs. applied departments. The "yrs.since.phd" gives the number of years since the respondent graduated with their Ph.D., while the "yrs.service" gives the number of years the respondent has been working at the institution. The "sex" variable has very little information, and only states that it takes the values Female and Male, and it may be that this refers to the gender identity of the respondent. Finally, the variable "salary" is simply the 9-month salary, reported in USD.

To get started, you should read the data set Salaries2.csv into R. The data set can be imported into R using the code below. Modify the text "..." to specify the location where you have saved the data file Salaries2.csv.

salary = read.csv(".../Salaries2.csv")

(a)

As a first step in this analysis, let's simply describe the main quantitative variable in this dataset, salary. The full description should include a nice visualization (properly labeled and titled), and any important basic statistical summaries. Write a few sentences summarizing the description of the variable and its distribution. (Round your answers to the nearest dollar where appropriate.)

The distribution of salaries is slightly

. The histogram indicates that the center of the distribution is slightly above

. The average 9-month salary (in dollars) is $

, while the median salary (in dollars) is $

. The salaries (in dollars) range from a low of $ to a high of $ .

(b)

As stated above, the main goal of this data collection effort is to monitor gender-based discrepancies in salary. Describe any such differences that are present in this dataset. You should include the appropriate comparative visualization, and descriptive statistics for each of the two reported genders that are available in the "sex" variable. Describe what these results tell you.

Based on the comparative boxplot and descriptive statistics, we can see that the median salary for female professors is the median salary for male professors; the upper and lower fourths of salaries for female professors are the respective upper and lower fourths of salaries for male professors; the distributions for both genders are ; and the distribution of salaries for professors has a wider range, with a smaller minimum and larger maximum, as well as showing evidence of a few large outliers.

(c)

Now let's try to find some of the factors that may be accounting for some of the differences observed above. A first obvious choice is "rank." If more men are being promoted, for example, then it stands to reason that they would have higher salaries due to that fact. Let's determine if there are gender differences between the ranks. Create the appropriate two-way tables of counts and proportions to explore this relationship.

Complete the table by specifying the number of professors of each reported gender at each of the ranks.

	rank
sex	AssocProf	AsstProf	Prof
Female
Male

Complete the table by specifying the proportion of female professors who are associate professors, assistant professors, and full professors respectively. Then specify the proportion of male professors who are associate professors, assistant professors, and full professors respectively. (Round your answers to four decimal places.)

	rank
sex	AssocProf	AsstProf	Prof
Female	0.0000		0.0000
Male	0.0000

Describe what these tell you.

It appears that there are gender differences with a higher proportion of male professors at the full professor rank than female professors and a higher proportion of female professors in each of the lower two ranks. It appears that there are gender differences with a higher proportion of female professors in each of the two higher ranks (full professor and associate professor) than male professors and a higher proportion of male professors at the assistant professor rank. It appears that there are gender differences with a higher proportion of male professors in each of the two higher ranks (full professor and associate professor) than female professors and a higher proportion of female professors at the assistant professor rank. It appears that there are gender differences with a higher proportion of female professors at the full professor rank than male professors and a higher proportion of male professors in each of the lower two ranks. It appears that there is no gender difference and the proportion of professors in each of the ranks is roughly the same within each gender.

(d)

Now let's verify that/determine the extent to which salaries differ by rank. Construct an appropriate comparative visualization, and calculate statistical summaries within each subgroup. Write a few sentences that summarize what you learn from this. (Round your answers to the nearest dollar where appropriate.)

Using R we find that the average salary (in dollars) for assistant professors is $ , the average salary (in dollars) for associate professors is $ , and the average salary (in dollars) for full professors is $ . These results indicate that, among professors in the data set, the average salary tends to as rank increases. We can also use R to find the standard deviation of salaries within each of the three ranks. The standard deviation in the salaries of assistant professors (in dollars) is $ , the standard deviation in the salaries for associate professors (in dollars) is $ , and the standard deviation in the salaries for full professors (in dollars) is $ . These results indicate that, among professors in the data set, the variation in salaries tends to as rank increases.

(e)

Given discrepancies in both salary by gender, salary by rank, and in representation of the genders in ranks, a better comparison might be to only compare the genders within specific ranks. Create three subsets according to the ranks, and within each subset generate an appropriate comparative visual, being sure to label and title it descriptively. In addition, calculate appropriate statistical summaries of the salary data. Write a few sentences to describe what you've learned from these within-rank comparisons of the genders. (Round your answers to the nearest dollar where appropriate.)

Among assistant professors, we see the difference (in dollars) in the average salaries of female and male professors (calculated as male − female) is $ . Among associate professors, the difference in means (in dollars) is $ . Among full professors, we see a difference (in dollars) of $ . The overall difference (across all ranks) in the average salaries (in dollars) of male and female professors (calculated as male − female) is $ . Thus, we find the difference in the overall mean salaries of male and female professors is the largest difference in salaries when calculated within each rank. We know male professors are at the higher ranks, which helps explain why we see different results when taking the overall difference in mean salaries across all ranks than when we examine the differences in the mean salaries of the two reported genders within each rank.

(f)

Now let's analyze differences between the two self reported genders by looking at them within the two levels of the discipline variable.

Complete the table by specifying the number of professors of each reported gender in each of the disciplines.

	discipline
sex	A	B
Female
Male

Complete the table by specifying the proportion of female professors who are in theoretical disciplines and the proportion of female professors who are in applied disciplines. Then specify the proportion of male professors who are in theoretical field and the proportion of male professors who are in applied fields. (Round your answers to four decimal places.)

	discipline
sex	A	B
Female		0.0000
Male	0.0000

Describe what these tell you.

The results tell us that there are far more female professors than male professors, but that proportions of professors in each of the disciplines are roughly the same for both reported genders. The results tell us that the number of professors identifying with each gender are roughly the same, but male professors are much more likely to work in applied departments whereas female professors are much more likely to work in theoretical departments. The results tell us that the number of professors identifying with each gender are roughly the same, but female professors are much more likely to work in applied departments whereas male professors are much more likely to work in theoretical departments. The results tell us that there are far more male professors than female professors, but that proportions of professors in each of the disciplines are roughly the same for both reported genders.

Using appropriate comparative visualizations and descriptive statistics compare the salaries of professors within applied and theoretical departments. Write a few sentences that summarize what you learn from this. (Round your answers to the nearest dollar where appropriate.)

Among the faculty in the data set, the average salary of professors in theoretical departments (in dollars) was found to be $ while the average salary of professors in applied departments (in dollars) was $ . Thus we find that professors in theoretical departments tend to have , on average, than professors in applied disciplines. Examining further, we find the standard deviation of salaries for professors in theoretical disciplines (in dollars) is $ and the standard deviation of salaries for professors in applied discplines (in dollars) is $ . So, we can see the variation in salaries is .

Given discrepancies in both salary by gender and salary by discipline a better comparison might be to only compare the genders within specific disciplines. Create two subsets according to the disciplines, and within each subset generate an appropriate comparative visual, being sure to label and title it descriptively. In addition, calculate appropriate statistical summaries of the salary data. Write a few sentences to describe what you've learned from these within-rank comparisons of the genders. (Round your answers to the nearest dollar where appropriate.)

Among professors in theoretical, fields we see the difference in the average salaries (in dollars) of female and male professors (calculated as male − female) is $ . In the applied disciplines, the difference in the average salaries of female and male professors (in dollars) is $ . The difference in average salaries between male and female professors in theoretical fields is than the overall difference in the average salaries of male and female professors. The difference in average salaries between male and female professors in applied fields is than the overall difference in the average salaries of male and female professors.

(g)

Summarize everything you've learned from the exploration of ths data.

From the analysis, we have seen that overall the average salary of female professors is the average salary of male professors. In addition, we have seen that male professors are likely to occupy the higher ranks than female professors, and that salary as rank increases. Within each rank, the differences in the average salaries between the genders tended to be the overall average difference in salaries. The results showed that there were . They also showed that the proportion of female professors working in applied disciplines was the proportion of male professors working in applied fields. The average salary for professors working in applied fields is the average salary for professors working in theoretical disciplines. Finally, we saw that the difference in average salary between male and female professors is greater in the disciplines.

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5. 3/3 points | Previous Answers DevoreStat9 1.CE.001.CV. My Notes

6. 1/20 points | Previous Answers DevoreStat9 4.SYS.002.S. My Notes

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Instructions

Select Your Scenario:

This problem contains data for 3 different scenarios: Travel and Tourism, Business, and Sports.

Read the scenarios, and once finished, you will be asked to select which scenario you would like to be assessed on.

You will not be asked to answer questions for the other 2 scenarios.

Travel and Tourism

When you travel by airplane, have you ever wondered about whether your flight might be delayed from taking off or from landing? This is an important consideration as you will need to arrange transportation to your final destination after you arrive at the airport. To help track airline performance, the U.S. Bureau of Transportation Statistics of the Department of Transportation publishes statistics. For the purposes of this dataset, a flight is considered delayed if it arrived at (or departed from) the gate 15 minutes or more after the scheduled arrival (or departure) time as reflected in the Computerized Reservation System.

We will explore the distribution of monthly percentage of domestic flights delayed in the United States using a sample of data for the years 2010 through 2019 by making a histogram with bins starting at 9% and a bin width of 3%. We will then determine the z-scores for a delayed percentage of (a) 17% and (b) 25%.

The dataset consists of the percentage of flights delayed for each month for years 2010 through 2019 for domestic flights in the United States.

†Airline Performance: Bureau of Transportation Statistics. (2020, September 1). On-Time Performance - Flight Delays at a Glance. United States Department of Transportation. https://www.transtats.bts.gov/HomeDrillChart.asp
Year	Month	Delayed (%)
2010	January	18.58
2010	February	19.66
2010	March	18.3
2010	April	13.83
2010	May	18.55

Business

Undergraduate business students at a public university in the midwestern United States ran a café one semester and collected data each business day to help make sound business decisions and to be more profitable. Among other things, the daily total cash register sales were recorded.

We will explore the distribution of daily total sales for this café using a sample of data from one semester by making a histogram of Sales ($) with bins starting at $60 and a bin width of $25. We will then determine the z-scores for a day when total sales were (a) $190 and (b) $105.

The dataset consists of data recorded across one semester including an index number that puts the observations in chronological order, the day of the week, and the total sales in dollars.

†http://jse.amstat.org/jse_data_archive.htm
Index	Day of Week	Sales($)
1	Tuesday	199.95
2	Wednesday	195.74
3	Thursday	102.68
4	Friday	162.88
5	Monday	101.76

Sports

It goes without saying that professional basketball players are tall. Height obviously matters when it comes to playing basketball and tall people are more efficient because they can reach the basket easily, allowing for more points per game, as well as more rebounds and blocked shots. If you watch National Basketball Association (NBA) games regularly, you certainly notice that many players are quite tall.

We will explore the distribution of NBA player heights using a sample of players active in the 2019-2020 season by making a histogram of "HEIGHT (INCHES)" with bins stating at 68 inches and a bin width of 2 inches. We will then determine the z-scores for players who are (a) 72 inches (6'0") and (b) 84 inches (7'0").

The dataset consists of the NBA player's name, team, and height, measured in inches, for players active in the 2019-2020 season.

†https://www.nba.com/stats/players/bio/
Player	Team	Height (Inches)
Aaron Gordon	ORL	80
Aaron Holiday	IND	73
Abdel Nader	OKC	77
Adam Mokoka	CHI	77
Admiral Schofield	WAS	77

Click the link below to begin the question by choosing a topic.

Pick your topic.

Choose the topic on which you would like to be assessed. Once you select your scenario, you cannot change your topic.

Travel and Tourism Business correct

Sports

Note: If you select Skip, you will be assessed on the Travel and Tourism topic.

Instructions

Select Your Scenario:

First, select the tab that corresponds to the topic you chose above.

Note: Click the SALT button in the tab corresponding to the topic you chose.

Travel and Tourism

When you travel by airplane, have you ever wondered about whether your flight might be delayed from taking off or from landing? This is an important consideration as you will need to arrange transportation to your final destination after you arrive at the airport. To help track airline performance, the U.S. Bureau of Transportation Statistics of the Department of Transportation publishes statistics. For the purposes of this dataset, a flight is considered delayed if it arrived at (or departed from) the gate 15 minutes or more after the scheduled arrival (or departure) time as reflected in the Computerized Reservation System.

We will explore the distribution of monthly percentage of domestic flights delayed in the United States using a sample of data for the years 2010 through 2019 by making a histogram with bins starting at 9% and a bin width of 3%. We will then determine the z-scores for a delayed percentage of (a) 17% and (b) 25%.

The dataset consists of the percentage of flights delayed for each month for years 2010 through 2019 for domestic flights in the United States.

†Airline Performance: Bureau of Transportation Statistics. (2020, September 1). On-Time Performance - Flight Delays at a Glance. United States Department of Transportation. https://www.transtats.bts.gov/HomeDrillChart.asp
Year	Month	Delayed (%)
2010	January	18.58
2010	February	19.66
2010	March	18.3
2010	April	13.83
2010	May	18.55

Import the dataset into SALT for analyzing.

A button hyperlink to the SALT program that reads: Use SALT.

Business

Undergraduate business students at a public university in the midwestern United States ran a café one semester and collected data each business day to help make sound business decisions and to be more profitable. Among other things, the daily total cash register sales were recorded.

We will explore the distribution of daily total sales for this café using a sample of data from one semester by making a histogram of Sales ($) with bins starting at $60 and a bin width of $25. We will then determine the z-scores for a day when total sales were (a) $190 and (b) $105.

The dataset consists of data recorded across one semester including an index number that puts the observations in chronological order, the day of the week, and the total sales in dollars.

†http://jse.amstat.org/jse_data_archive.htm
Index	Day of Week	Sales($)
1	Tuesday	199.95
2	Wednesday	195.74
3	Thursday	102.68
4	Friday	162.88
5	Monday	101.76

Import the dataset into SALT for analyzing.

Sports

It goes without saying that professional basketball players are tall. Height obviously matters when it comes to playing basketball and tall people are more efficient because they can reach the basket easily, allowing for more points per game, as well as more rebounds and blocked shots. If you watch National Basketball Association (NBA) games regularly, you certainly notice that many players are quite tall.

We will explore the distribution of NBA player heights using a sample of players active in the 2019-2020 season by making a histogram of "HEIGHT (INCHES)" with bins stating at 68 inches and a bin width of 2 inches. We will then determine the z-scores for players who are 72 inches (6'0") and (b) 84 inches (7'0").

The dataset consists of the NBA player's name, team, and height, measured in inches, for players active in the 2019-2020 season.

†https://www.nba.com/stats/players/bio/
Player	Team	Height (Inches)
Aaron Gordon	ORL	80
Aaron Holiday	IND	73
Abdel Nader	OKC	77
Adam Mokoka	CHI	77
Admiral Schofield	WAS	77

Import the dataset into SALT for analyzing.

After you have clicked the tab for your selected topic and read the problem, answer the questions below.

(a)

Use SALT to summarize the data and fill in the following table, rounding values to four decimal places as needed.

Variable	N	Mean	Standard Deviation	Median	Minimum Value	Maximum Value
Numerical Variable

(b)

Create a histogram with "Starting Point" and "Bin/Class Width" values asked for.

The distribution for this variable mound shaped and at least roughly symmetric.

(c)

Determine the relative standing for the two data values of interest using the z-score formula appropriate for samples. Round your answers to two decimal places.

Data value (a).

z

=

x − x

s

=

Data value (b).

z

=

x − x

s

=

Data value (a) is standard deviations the mean whereas data value (b) is standard deviations the mean. (Remember to take the absolute value of the z-score to determine the number of standard deviations each data value is away from the mean.)

(d)

Most data points are within three standard deviations of the mean. In other words, most observations will have a z-score that is larger than 3 and less than 3.

Find the data value with a z-score of −3, rounded to two decimal places.

x	=	z · s + x

	=

Find the data value with a z-score of 3, rounded to two decimal places.

x	=	z · s + x

	=

Our sample's minimum value further than 3 standard deviations below the mean. Our sample's maximum further than 3 standard deviations above the mean. Upon further inspection of the histogram in SALT it can be observed that observations would have a z-score between −3 and 3.

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7. 2/2 points | Previous Answers DevoreStat9 4.AE.006. My Notes

Example 4.6

Let X, the thickness of a certain metal sheet, have a uniform distribution on [A, B]. The density function is shown below. For x < A, F(x) =

, since there is no area under the graph of the density function to the left of such an x. For x ≥ B, F(x) =

, since all the area is accumulated to the left of such an x. Finally, for A ≤ x ≤ B,

F(X) =

x	f(y)dy

−∞

=

x

1

B − A

dy

A

=

1

B − A

· y

y=x

y=A

=

x − A

B − A

The entire cdf is

F(x) =

0

x < A

x − A

B − A

A ≤ x < B

1

x ≥ B

The graph of this cdf appears below.

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8. 5/5 points | Previous Answers DevoreStat9 4.E.005. My Notes

A college professor never finishes his lecture before the end of the hour and always finishes his lectures within 2 min after the hour. Let X = the time that elapses between the end of the hour and the end of the lecture and suppose the pdf of X is as follows.

f(x) =

kx²		0 ≤ x ≤ 2
0		otherwise

(a) Find the value of k. (Enter your answer to three decimal places.)

Draw the corresponding density curve. [Hint: Total area under the graph of f(x) is 1.]

(b) What is the probability that the lecture ends within 1 min of the end of the hour? (Enter your answer to three decimal places.)

(c) What is the probability that the lecture continues beyond the hour for between 30 and 90 sec? (Round your answer to four decimal places.)

(d) What is the probability that the lecture continues for at least 105 sec beyond the end of the hour? (Round your answer to four decimal places.)

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9. 3/6 points | Previous Answers DevoreStat9 4.E.022. My Notes

The weekly demand for propane gas (in 1000s of gallons) from a particular facility is an rv X with the following pdf.

f(x) =

2

1 −

1

x²

1 ≤ x ≤ 2

0

otherwise

(a) Compute the cdf of X.

F(x) =

0

x < 1

2(x +1x−2)

1 ≤ x ≤ 2

1

2 > x

(b) Obtain an expression for the (100p)th percentile.
η(p) =

What is the value of mu tilde

? (Round your answer to three decimal places.)

(c) Compute E(X) and V(X). (Round your answers to four decimal places.)

E(X)	= thousand gallons
V(X)	= thousand gallons squared

(d) If 1.4 thousand gallons are in stock at the beginning of the week and no new supply is due in during the week, how much of the 1.4 thousand gallons is expected to be left at the end of the week? [Hint: Let h(x) = amount left when demand = x.] (Round your answer to three decimal places.)
thousand gallons

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10. 3/3 points | Previous Answers DevoreStat9 4.E.040.S. My Notes

An article suggested that yield strength (ksi) for A36 grade steel is normally distributed with μ = 44 and σ = 5.0.

(a) What is the probability that yield strength is at most 39? Greater than 62? (Round your answers to four decimal places.)

at most 39
greater than 62

(b) What yield strength value separates the strongest 75% from the others? (Round your answer to four decimal places.)

ksi

You may need to use the appropriate table in the Appendix of Tables to answer this question.

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11. 6/6 points | Previous Answers DevoreStat9 4.E.069. My Notes

12. 6/6 points | Previous Answers DevoreStat9 4.E.094.S. My Notes

13. 8/8 points | Previous Answers DevoreStat9 12.E.014.MI.S. My Notes

The efficiency for a steel specimen immersed in a phosphating tank is the weight of the phosphate coating divided by the metal loss (both in mg/ft²). An article gave the accompanying data on tank temperature (x) and efficiency ratio (y).

Temp.	173	175	176	177	177	178	179	180
Ratio	0.92	1.29	1.50	0.95	0.97	1.18	0.94	1.88

Temp.	183	183	183	183	183	184	184	185
Ratio	1.49	1.62	1.71	2.11	2.07	0.90	1.39	1.00

Temp.	185	185	185	187	187	188	189	191
Ratio	1.71	2.02	2.66	1.51	2.54	3.10	1.89	3.14

(a)

Determine the equation of the estimated regression line. (Round all numerical values to four decimal places.)

y =

−15.9238+0.0965x

(b)

Calculate a point estimate for true average efficiency ratio when tank temperature is 185. (Round your answer to four decimal places.)

(c)

Calculate the values of the residuals from the least squares line for the four observations for which temperature is 185. (Round your answers to two decimal places.)

(185, 1.00)

(185, 1.71)

(185, 2.02)

(185, 2.66)

Why do they not all have the same sign?

These residuals do not all have the same sign because in the cases of the first two pairs of observations, the observed efficiency ratios were smaller than the predicted value. In the cases of the last two pairs of observations, the observed efficiency ratios were larger than the predicted value. These residuals do not all have the same sign because in the case of the third pair of observations, the observed efficiency ratio was equal to the predicted value. In the cases of the other pairs of observations, the observed efficiency ratios were smaller than the predicted value. These residuals do not all have the same sign because in the cases of the first two pairs of observations, the observed efficiency ratios were larger than the predicted value. In the cases of the last two pairs of observations, the observed efficiency ratios were smaller than the predicted value. These residuals do not all have the same sign because in the case of the second pair of observations, the observed efficiency ratio was equal to the predicted value. In the cases of the other pairs of observations, the observed efficiency ratios were larger than the predicted value.

(d)

What proportion of the observed variation in efficiency ratio can be attributed to the simple linear regression relationship between the two variables? (Round your answer to three decimal places.)

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14. 2/4 points | Previous Answers DevoreStat9 6.CE.501.XP.SIP. My Notes

15. –/18 points DevoreStat9 PJT.1.001. My Notes

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Milestone 1: Research Design

Question 1

What is your research question?

Your research question should be based on a topic that interests you and that you can reasonably obtain data for. Try to make your research question as specific as possible. Form a research question about a population that you will be able to sample. Some examples of research questions are: "Are students at my college able to taste the difference between regular coffee and decaffeinated coffee?", "Does the GPA, age, and number of credits needed for graduation for juniors at my university differ between transfer students and non-transfer students?", "Have the new water rates in my water district changed residents' water usage habits?", and "Do recent graduates from the business department at my university get larger starting salaries on average if they have participated in a summer internship?"

This answer has not been graded yet.
Question 2

Has any research already been done that might help with your project?

You can search your university's online database to find articles that discuss research that has already been done on your research question. Please make note of any articles or other sources that helped guide your research question and research design. You will be asked to provide references to any sources you used.

This answer has not been graded yet.
Question 3

What is your population of interest?

Your population of interest will be closely related to your research question. For instance, if you are testing the freshman 15 theory and you believe that students at your college do not gain 15 pounds on average over the course of freshman year, then your population of interest is the students at your college who have completed freshman year.

This answer has not been graded yet.
Question 4

Describe your sampling plan.

You want to ensure that your sample is representative of the population of interest. How will you target your population of interest? Sampling involves tradeoffs; you may have to settle for a convenience sample, which is fine for this project as long as you acknowledge this. Sampling is about doing the best you can with the resources you have at your disposal.

This answer has not been graded yet.
Question 5

Will this sample be representative of the population of interest? If so, why? If not, what population will the sample be representative of?

Is there any group of people within the population of interest that your sampling plan is likely to miss? For instance, if you are using a random sample of landline telephone numbers from your state in order to achieve a random sample of residents in your state, then you are missing all of the residents of your state who only have a cell phone and do not have a landline. Or, if your population of interest is all adults in your country, but you only conduct interview of adults from your local community, then your sample is only representative of the adults in your local community.

This answer has not been graded yet.

Question 6

What variables will you measure?

Make sure that the variables you choose are measurable. If you are performing an experiment where you are comparing two skin creams to determine which gives the skin a more youthful glow, how exactly will you measure "youthful glow"? Are there other variables that you will collect because they too may be of interest? Age? Gender? Level of education? Is your variable type numeric or categorical? If your variable type is numeric, is it discrete or continuous? Do your variables need to be measured using special equipment?

Variable	Type	How will you measure it?
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Question 7

Describe your study design.

Will you be conducting an observational study or performing an experiment? What will your sample size be? If you will be performing an experiment, will there be a placebo? If so, describe the placebo. Will the experiment be blinded? Double-blinded? Who will carry out the experiment and how?

This answer has not been graded yet.

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Devore-Probability&Statistics for Engineering 9/e (Homework)

Current Score : 47 / 155

Due : Sunday, January 27, 2030 23:30 EST

Last Saved : n/a Saving... ()

Instructions

Assignment Submission

Assignment Scoring

Stats in Practice

Part I - Multiple Choice Questions

Part II - Discussion Question

Milestone 1: Research Design

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

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Welcome, demo@demo

Devore-Probability&Statistics for Engineering 9/e (Homework)

Current Score : 47 / 155

Due : Sunday, January 27, 2030 23:30 EST

Last Saved : n/a Saving... ()

Instructions

Assignment Submission

Assignment Scoring

Stats in Practice

Part I - Multiple Choice Questions

Part II - Discussion Question

Milestone 1: Research Design

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7