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Moore - Intro to the Practice of Statistics 9/e (Homework)

James Finch

Statistics, section 2, Fall 2019

Instructor: Dr. Friendly

Current Score : 20 / 82

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

Last Saved : n/a Saving...  ()

Question
Points
1 2 3 4 5 6 7 8
15/19 –/4 –/5 3/3 2/2 –/23 –/11 –/15
Total
20/82 (24.4%)
  • Instructions

    Introduction to the Practice of Statistics (IPS), 9th edition, by David S. Moore, George P. McCabe, and Bruce A. Craig and published by W. H. Freeman shows students how to produce and interpret data from real-world contexts—doing the same type of data gathering and analysis that working statisticians in all kinds of businesses and institutions do every day. With this phenomenally successful approach originally developed by David Moore and George McCabe, statistics is more than just a collection of techniques and formulas. Instead, students develop a systematic way of thinking about data, with a focus on problem-solving that helps them understand statistical concepts and master statistical reasoning.

    Question 1 features a randomized data table where a student selects boxplot graphs and fills in a stem-and-leaf display based on their unique set of values.

    Question 2 demonstrates a scatter plot and grading for the coefficients of a linear regression line, allowing for potential partial credit.

    Question 3 exhibits a tutorial for finding probabilities based on given figures displaying the uniform density curve.

    Question 4 utilizes the format for a confidence interval and margin of error interpretation.

    Question 5 contains the t-distribution critical values table and directs students to illustrate values of a test statistic as a comma-separated answer list with rounding.

    Question 6 showcases students entering table values to analyze data with multiple summary conclusions, illustrating an open-ended format.

    Question 7 highlights multiple part questions addressing the ANOVA statistic, degrees of freedom, and approximating a P-value using a table or statistical program.

    Question 8 includes a downloadable data set for students to analyze and perform hypothesis tests. 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.

    The answer key and solutions will display after the first submission for demonstration purposes. Instructors can configure these to display after the due date or after a specified number of submissions.

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. 15/19 points  |  Previous Answers MIntroStat9 1.E.070. My Notes
Question Part
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1/1 1/1 1/1 /1 1/1 1/1 0/1 1/1 1/1 1/1 1/1 1/1 1/1 0/1 1/1 0/1 1/1 1/1 1/1
1/100 1/100 1/100 0/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100
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15/19
 
Smolts are young salmon at a stage when their skin becomes covered with silvery scales and they start to migrate from freshwater to the sea. The reflectance of a light shined on a smolt's skin is a measure of the smolt's readiness for the migration. Here are the reflectances, in percents, for a sample of 50 smolts.

57.6 54.9 63.4 57.0 54.7 42.3 63.6 55.4 33.5 63.4
58.4 42.2 56.0 47.9 56.0 55.8 38.9 49.8 42.4 45.5
69.0 50.4 53.0 38.3 60.5 49.3 42.7 44.5 46.4 44.4
58.8 42.0 47.7 47.9 69.2 46.7 68.1 42.9 45.6 47.2
59.7 37.8 54.0 43.1 51.3 64.4 43.8 42.6 50.8 43.9

(a) Find the IQR for the smolt data.


(b) Use the 1.5 IQR rule to identify any outliers. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
DNE


(c) Make a boxplot for the smolt data.



(d) Make a modified boxplot for these data.


Describe the distribution using only the information in the boxplot. (Select all that apply.)
Since there are outliers, there a need for a modified boxplot. The distribution is roughly symmetric with near 50. The is about 33, and the about 68. The are about 43 and 57.

(e) Make a stemplot for these data. (Plot only the integer values of the numbers presented, with the stem being the tens' place and the leaf being the ones' place. Split each stem in two, with leaves ranging from 0 to 4 on the first stem and 5 to 9 on the second. Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.)
        
3
3
4
4
5
5
6
6

(f) Compare the boxplot, the modified boxplot, and the stemplot. Evaluate the advantages and disadvantages of each graphical summary for describing the distribution of the smolt reflectance data.

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2. /4 points MIntroStat9 2.E.086. My Notes
Question Part
Points
Submissions Used
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/1 /1 /1 /1
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/4
 
Every few years, the National Assessment of Educational Progress asks a national sample of eighth-graders to perform the same math tasks. The goal is to get an honest picture of progress in math. Suppose these are the last few national mean scores, on a scale of 0 to 500.
Year 1990 1992 1996 2000 2003 2005 2008 2011 2013
Score 263 267 273 274 278 279 281 287 289
(a) Make a time plot of the mean scores, by hand. This is just a scatterplot of score against year. There is a slow linear increasing trend.


(b) Find the regression line of mean score on time step-by-step. First calculate the mean and standard deviation of each variable and their correlation (use a calculator with these functions). Then find the equation of the least-squares line from these. (Round your answers to two decimal places.)
ŷ = + x

Draw the line on your scatterplot. What percent of the year-to-year variation in scores is explained by the linear trend? (Round your answer to one decimal place.)
%
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3. /5 points MIntroStat9 4.E.058.Tut. My Notes
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1 2 3 4 5
/1 /1 /1 /1 /1
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/5
 
Let the random variable X be a random number with the uniform density curve in the figure below. Find the following probabilities.
WebAssign Plot
(a)
P(X 0.25)
(b)
P(X = 0.25)
(c)
P(0.25 < X < 1.35)
(d)
P(0.19 X 0.23 or 0.5 X 0.8)
(e)
X is not in the interval 0.4 to 0.8.
Tutorial
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4. 3/3 points  |  Previous Answers MIntroStat9 6.E.012. My Notes
Question Part
Points
Submissions Used
1 2 3
1/1 1/1 1/1
1/100 1/100 1/100
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3/3
 
A study of stress on the campus of your university reported a mean stress level of 78 (on a 0 to 100 scale with a higher score indicating more stress) with a margin of error of 3 for 95% confidence. The study was based on a random sample of 64 undergraduates.
(a)
Give the 95% confidence interval.
Correct: Your answer is correct. seenKey

75

, Correct: Your answer is correct. seenKey

81

(b)
If you wanted 99% confidence for the same study, would your margin of error be greater than, equal to, or less than 3? Explain your answer.
     Correct: Your answer is correct.
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5. 2/2 points  |  Previous Answers MIntroStat9 7.E.016. My Notes
Question Part
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1 2
1/1 1/1
1/100 1/100
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2/2
 
Assume a sample size of n = 23. Draw a picture of the distribution of the t statistic under the null hypothesis. Use Table D and your picture to illustrate the values of the test statistic that would lead to rejection of the null hypothesis at the 5% level for a two-sided alternative.

Correct: Your answer is correct.
What is/are the value(s) of the critical t in this case? (Enter your answer as a comma-separated list using three decimal places.)
2.074, 2.074
Correct: Your answer is correct. webMathematica generated answer key
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6. /23 points MIntroStat9 9.E.049. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
/1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1
0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100
Total
/23
 
A survey of 13,374 students in a country who enrolled in private career colleges was conducted to understand student participation in the private postsecondary educational system. In one part of the survey, students were asked about their field of study and about when they entered college. Here are the results.
Field of
Study
Number of
Students
Time of Entry
Right After High School Later
Trades 952 34% 66%
Design 564 47% 53%
Health 5095 40% 60%
Media/IT 3138 31% 69%
Service 1380 36% 64%
Other 2245 52% 48%
In this table, the second column gives the number of students in each field of study. The next two columns give the marginal distribution of time of entry for each field of study.
(a) Use the data provided to make the 6 2 table of counts for this problem. (Enter your answer to the nearest integer.)
     Time of Entry
Field of Study Right After High School      Later
Trades
Design
Health
Media/IT
Service
Other

(b) Analyze the data. (Round your numerical answers to one decimal place.)
The most popular field of study is with % of these students. The least popular field of study is with % of these students. Overall % of these students enrolled right after high school.

(c) Write a summary of your conclusions. Be sure to include the results of your significance testing. (Use α = 0.01.)

State the null and alternative hypotheses.

Null Hypothesis:
    

Alternative Hypothesis:
    

State the χ2 statistic, degrees of freedom, and the P-value. (Round your answer for χ2 to one decimal place and your P-value to four decimal places.)
χ2 =
df =
P-value =

Conclusion:
    
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7. /11 points MIntroStat9 12.E.033. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8 9 10 11
/1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1
0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100
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/11
 
University and college food service operations have been trying to keep up with the growing expectations of consumers with regard to the overall campus dining experience. Because customer satisfaction has been shown to be associated with repeat patronage and new customers through word-of-mouth, a public university in the Midwest took a sample of patrons from their eating establishments and asked them about their overall dining satisfaction. The following table summarizes the results for three groups of patrons.
Category
x
n
s
StudentMeal Plan 3.44 489 0.804
FacultyMeal Plan 3.69 69 0.824
StudentNo Meal Plan 3.47 212 0.657
(a)
Is it reasonable to use a pooled standard deviation for these data? Why or why not?
    
If it is reasonable, compute the standard deviation. (Round your answer to four decimal places. If it is not reasonable, enter NONE.)
(b)
The ANOVA F statistic was reported as 3.202. What are the degrees of freedom?
DFG = DFE =
Find either an approximate (from a table) or an exact (from software) P-value. Sketch a picture of the F distribution that illustrates the P-value.

What do you conclude?
    
(c)
Prior to performing this survey, food service operations thought that satisfaction among faculty would be higher than satisfaction among students. Use the results in the table to test this contrast. Make sure to specify the null and alternative hypotheses, test statistic, and P-value.
Let
μ1
represent the population mean for students with a meal plan,
μ2
represent the population mean for faculty with a meal plan, and
μ3
represent the population mean for students with no meal plan.
Choose the appropriate contrast.
    
Specify the null and alternative hypotheses.
    
Calculate the test statistic. (Round your answer to three decimal places.)
t =
Compute the P-value.
    
State your conclusion.
    
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8. /15 points MIntroStat9 12.E.065. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
/1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1
0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100
Total
/15
 
Many studies have suggested that there is a link between exercise and healthy bones. Exercise stresses the bones and this causes them to get stronger. One study examined the effect of jumping on the bone density of growing rats. There were three treatments: a control with no jumping, a low-jump condition (the jump height was 30 centimeters), and a high-jump condition (60 centimeters). After 8 weeks of 10 jumps per day, 5 days per week, the bone density of the rats (expressed in mg/cm3 ) was measured. Here are the data. data94.dat
(a) Make a table giving the sample size, mean, and standard deviation for each group of rats. Consider whether or not it is reasonable to pool the variances. (Round your answers for x, s, and s_(x^^\_) to one decimal place.)
Group n x^^\_ s s_(x^^\_)
Control
Low jump
High jump

(b) Run the analysis of variance. Report the F statistic with its degrees of freedom and P-value. What do you conclude? (Round your test statistic to two decimal places and your P-value to three decimal places.)
F =
P =
Conclusion: There is statistically significant difference between the three treatment means at the α = .05 level.
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