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Statistics, section 2, Fall 2019
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Utts and Heckard - Mind on Statistics 6/e (Homework)

James Finch

Statistics, section 2, Fall 2019

Instructor: Dr. Friendly

Current Score : 43 / 118

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

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

Ask Your Teacher Extension Requests Print Assignment

Question

Points

1	2	3	4	5	6	7	8	9	10	11	12	13	14
3/3	3/3	3/3	3/3	13/13	–/9	0/4	–/4	1/20	4/8	11/13	2/4	–/13	–/18

Total

43/118 (36.4%)

Instructions

Mind on Statistics, 6th Edition, written by Utts and Heckard and published by Cengage Learning, helps students develop a conceptual understanding of statistical ideas by showing them how to find meaning in data. This textbook engages students' curiosity with intriguing questions, and explains statistical topics in the context of interesting, useful examples, and case studies. The WebAssign component for this text engages students with an interactive eBook and a variety of textbook resources including concept videos and PowerPoint lectures slides.

Question 1 is an example of a Concept Video Question. (CV) Concept Video questions provide students with a Concept Video along with two to three comprehension questions. Concept Videos are 7-10 minutes in length and are designed to help students with big picture understanding of statistics.

Question 2 presents a frequency table for students to select the correct histogram among multiple choices, then summarize and comment on the data set. Students can use SALT to draw the graph.

Question 3 provides a scatter plot and asks students to answer questions about the data characteristics displayed in the graph.

Question 4 displays a data set with regression equation for the data and asks students to interpret and use the equation to make predictions.

Question 5 asks students to create a contingency table from a given scenario, then calculate percents of given outcomes to determine relationships between symptoms.

Question 6 asks students to find probabilities of a random variable and create the probability distribution function.

Question 7 asks students to use SALT to find binomial probabilities for a binomial random variable.

Question 8 asks students to use SALT to find normal probabilities for a normally distributed random variable.

Question 9 is an example of a new Select Your Scenario question type. (SYS) Select Your Scenario problems provide students with 3 different contexts to choose from. They select the scenario most relevant to them, and then solve the problem. Regardless of which scenario the student chooses, they will be required to answer questions demonstrating knowledge of a learning objective, making them the perfect questions to assign toward the end of a chapter. Students can use SALT to answer this question.

Question 10 asks students to use SALT to create 95% confidence intervals for the mean response for two independent treatment groups then determine if there is a difference between the treatments.

Question 11 asks students to complete the steps for a one-proportion z-test. SALT is provided as support.

Question 12 is a Stats in Practice question that demonstrates the use of videos displayed within a question, followed by multiple-choice and discussion questions in a unique two-part accordion-style type of display.

Question 13 is an example of a Statistical Lab.

Question 14 highlights Milestone 1, the first step in presenting and tracking Project Milestones for a statistical research project. This demo assignment allows many submissions and allows you to try another version of the same question for practice wherever the problem has randomized values.

Assignment Submission

For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer.

Assignment Scoring

Your last submission is used for your score.

1. 3/3 points | Previous Answers UHStat6 1.CE.001.CV. My Notes

2. 3/3 points | Previous Answers UHStat6 2.4.044.S. My Notes

The following table summarizes diastolic blood pressures for a sample of 700 women aged 30 to 39 years old. Diastolic blood pressure is the second of the two values in a blood pressure measurement. The intervals in the table include the lower limit, but not the upper limit. For instance, someone with a value of 55 would be counted in the interval 55 to 65, not 45 to 55.

Diastolic B.P.	Frequency
45–55	8
55–65	77
65–75	263
75–85	251
85–95	73
95–105	25
105–115	3

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

(a)

Create a histogram for the diastolic blood pressures of the 700 women. (Because the data table has summarized the data into categories, use SALT to create a bar chart.)

A graph has a horizontal axis labeled "Diastolic B.P." with values from 45 to 115 and a vertical axis labeled "Percent" with values from 0% to 45%. The histogram has 7 bars of equal width. Each bar is associated with an interval and an approximate value as listed below.
45 to 55: 0%

55 to 65: 1%

65 to 75: 4%

75 to 85: 10%

85 to 95: 11%

95 to 105: 36%

105 to 115: 38%

(b)

Provide a summary of the dataset based on your histogram.

A majority of the women have a diastolic blood pressure between 65 and 85. With regard to shape, the data are slightly skewed to the left. A majority of the women have a diastolic blood pressure less than or equal to 65. With regard to shape, the data are strongly skewed to the right. A majority of the women have a diastolic blood pressure greater than or equal to 95. With regard to shape, the data are strongly skewed to the left. A majority of the women have a diastolic blood pressure greater than or equal to 95. With regard to shape, the data are strongly skewed to the right. A majority of the women have a diastolic blood pressure less than or equal to 65. With regard to shape, the data are strongly skewed to the left. A majority of the women have a diastolic blood pressure between 65 and 85. With regard to shape, the data are slightly skewed to the right.

(c)

Explain why you could not use the information in the table to create a stem-and-leaf plot for this dataset.

A stem-and-leaf plot presents all individual values, but we do not have the data in this form. A stem-and-leaf plot presents all individual values, and we do have the data in this form so we could create a stem-and-leaf plot. A stem-and-leaf plot presents a summary of the data, but we do not have the data in this form. A stem-and-leaf plot presents a summary of the data, and we do have the data in this form so we could create a stem-and-leaf plot.

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3. 3/3 points | Previous Answers UHStat6 3.1.008. My Notes

4. 3/3 points | Previous Answers UHStat6 3.2.018.QR. My Notes

Dataset temperature is available here.

The average August temperatures (y) and geographic latitudes (x) of 20 cities in the United States are given in the following table.

†Data source: The World Almanac and Book of Facts, 1999, pp. 220, 456. Reprinted by permission.
City	Latitude	Aug Temp
Miami, FL	26	83
Houston, TX	30	82
Mobile, AL	31	82
Dallas, TX	33	85
Phoenix, AZ	33	92
Los Angeles, CA	34	75
Memphis, TN	35	81
Norfolk, VA	37	77
San Francisco, CA	38	64
Baltimore, MD	39	76
Kansas City, MO	39	76
Washington, DC	39	74
Pittsburgh, PA	40	71
Cleveland, OH	41	70
New York, NY	41	76
Boston, MA	42	72
Syracuse, NY	43	68
Minneapolis, MN	45	71
Portland, OR	46	69
Duluth, MN	47	64

The regression equation for these data is expressed with the following formula.

ŷ = 113.584 − 1.006x

(a)

What is the slope of the line? Interpret the slope in terms of how mean August temperature is affected by a change in latitude.

For each one unit (measured in degrees) increase in latitude, average August temperature increases by 113.584 °F. For each one unit (measured in degrees) increase in latitude, average August temperature increases by 1.006°F. For each one unit (measured in degrees) increase in latitude, average August temperature decreases by 1.006°F. For each one unit (measured in degrees) decrease in latitude, average August temperature decreases by 1.006°F. For each one unit (measured in degrees) increase in latitude, average August temperature decreases by 113.584 °F.

(b)

Estimate the mean August temperature (in °F) for a city with latitude of 39. (Round your answer to two decimal places.)

°F

(c)

San Francisco CA has a mean August temperature of 64, and its latitude is 38. Use the regression equation to estimate the mean August temperature in San Francisco CA, and then calculate the prediction error (residual) for San Francisco CA (in °F). (Round your answer to two decimal places.)

°F

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5. 13/13 points | Previous Answers UHStat6 4.1.010. My Notes

Do grumpy old men have a greater risk of having coronary heart disease than men who aren't so grumpy? Researchers examined this question in a prospective observational study. For seven years, the researchers studied men between the ages of 46 and 90 years old. All study participants completed a survey of anger symptoms at the beginning of the study period. Among 203 men who had no anger symptoms, there were 11 cases of coronary heart disease. Among 541 men who had the most anger symptoms, there were 54 cases of coronary heart disease.

(a)

Construct a contingency table for the relationship between degree of anger and the incidence of heart disease.

	Heart Disease	No Heart Disease	Total
No Anger
Most Anger
Total

(b)

Among those with no anger symptoms, what percentage had coronary heart disease? (Round your answer to one decimal place.)

(c)

Among those with the most anger symptoms, what percentage had coronary heart disease? (Round your answer to one decimal place.)

(d)

Draw a bar graph of these data. Based on this graph, does there appear to be an association between anger and the risk of coronary heart disease? Explain.

There

to be a relationship. The percentage with heart disease is

for men with no anger symptoms compared to men with the most anger symptoms.

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6. –/9 points UHStat6 8.2.021. My Notes

A woman decides to have children until she has her first boy or until she has four children, whichever comes first. Let X = number of children she has. For simplicity, assume that the probability of a boy is .5 for each birth.

(a) The simple events in the simple space are {B, GB, GGB, GGGB, GGGG}, where we use B for boy and G for girl. For instance, one simple event is GB, because the woman quits once she has a boy. Find the probability for each of the simple events in the sample space.

P(B)	=
P(GB)	=
P(GGB)	=
P(GGGB)	=
P(GGGG)	=

(b) Find the probability distribution function for X.

k	1	2	3	4
P(X = k)

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7. 0/4 points | Previous Answers UHStat6 8.4.045.S. My Notes

Assuming that X is a binomial random variable with n = 10 and p = 0.25, find the probability, P for each of the following values of X. (Round your answers to five decimal places.)

(a) X = 5.
P(X = 5) =

(b) X = 2.
P(X = 2) =

(d) X = 8.
P(X = 8) =

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8. –/4 points UHStat6 8.6.075.S. My Notes

Suppose the yearly rainfall totals for a some city follow a normal distribution, with mean of 22 inches and standard deviation of 10 inches. For a randomly selected year, what is the probability, P, that total rainfall will be in each of the following intervals? (Round all answers to four decimal places.)

(a) Less than 8 inches.
P =

(b) Greater than 42 inches.
P =

(c) Between 12 and 32 inches.
P =

(d) Greater than 51 inches.
P =

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9. 1/20 points | Previous Answers UHStat6 8.6.SYS.002.S. My Notes

Question Part

Points

Submissions Used

1/1

–/1

1/5

0/5

Total

1/20

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) 15% and (b) 24%.

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) $210 and (b) $100.

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) 71 inches (5'11") 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 correct

Business 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

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.

Business

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

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).

x − x

Data value (b).

x − x

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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10. 4/8 points | Previous Answers UHStat6 11.2.032.S. My Notes

Volunteers who had developed a cold within the previous 24 hours were randomized to take either zinc or placebo lozenges every 2 to 3 hours until their cold symptoms were gone. Twenty-five participants took zinc lozenges, and 23 participants took placebo lozenges. The mean overall duration of symptoms for the zinc lozenge group was 3.5 days, and the standard deviation of overall duration of symptoms was 1.2 days. For the placebo group, the mean overall duration of symptoms was 8.5 days, and the standard deviation was 2 days.

(a)

Calculate a 95% confidence interval for the mean overall duration of symptoms if everyone in the population were to take the zinc lozenges. (Round your answers to two decimal places.)

days

(b)

Calculate a 95% confidence interval for the mean overall duration of symptoms if everyone in the population were to take the placebo lozenges. (Round your answers to two decimal places.)

days

(c)

On the basis of the intervals computed in parts (a) and (b), is it reasonable to conclude generally that taking zinc lozenges reduces the overall duration of cold symptoms more than if taking a placebo? Explain why you think this is or is not an appropriate conclusion.

reasonable to conclude that taking zinc lozenges reduces the duration of symptoms. The confidence intervals computed in parts (a) and (b) , so a reasonable conclusion is that in a population of cold sufferers the mean duration of symptoms if zinc lozenges are taken is than the mean duration if placebo is taken.

(d)

In their report, the researchers say that they checked whether it was reasonable to assume that the data were sampled from a normal curve population and decided that it was. How is this relevant to the calculations done in parts (a) and (b)?

For relatively samples such as these, a necessary condition (in theory) is that the population of measurements has a normal distribution.

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11. 11/13 points | Previous Answers UHStat6 12.2.058.S. My Notes

About 10% of the human population is left-handed. Suppose a researcher speculates that artists are more likely to be left-handed than other people in the general population. The researcher surveys 200 artists and finds that 26 of them are left-handed.

If we use p to represent the proportion of all artists who are left-handed, the hypotheses are

H₀: p = 0.10

and

H_a: p > 0.10.

The sample result was that 26 artists of 200 surveyed (or 13%) are left-handed.

(a)

From the given information, do we know if the conditions necessary to use a z-statistic for this test are met? Explain.

sure the sample was selected randomly, the sample size

large enough because both np and n(1 − p) are

10.

(b)

State the population of interest, the population parameter of interest, and the value of the sample statistic.

The population of interest is

. The population parameter is p =

. The sample statistic is

(c)

Conduct a hypothesis test using level of significance

α = 0.05.

Clearly give the details of the five steps. Be sure to write a conclusion.

Set up the null and alternative hypothesis.

H₀: p 0.1

H_a: p

0.1

Compute the test statistics for this situation. (Round your answer to two decimal places.)

z =

Calculate the p-value for the test. (Round your answer to four decimal places.)

p-value =

On the basis of the p-value, make a conclusion for this situation.

because the p-value is

than 0.05.

Write a conclusion to this situation in words.

conclude that artists are more likely to be left-handed than people in the general population.

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12. 2/4 points | Previous Answers UHStat6 10.CE.002.SIP. My Notes

13. –/13 points UHStat6 16.Lab.001.Excel. My Notes

14. –/18 points UHStat6 PJT.1.001. My Notes

Question Part

Points

Submissions Used

–/1

0/5

Total

–/18

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?
		This answer has not been graded yet.
		This answer has not been graded yet.
		This answer has not been graded yet.
		This answer has not been graded yet.

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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Home My Assignments Extension Request

Utts and Heckard - Mind on Statistics 6/e (Homework)

Current Score : 43 / 118

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

Statistical Lab

Background

Guidelines

About the Data

Tech Guide

General Notes

Lab Questions

References

Milestone 1: Research Design

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

1	2	3
1/1	1/1	1/1
2/5	3/5	2/5

1	2	3	4
0/1	0/1	0/1	0/1
1/5	1/5	1/5	1/5