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Statistics, section 2, Fall 2019
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Peck, Short & Olsen - Intro to Statistics (AP) 6/e (Homework)

James Finch

Statistics, section 2, Fall 2019

Instructor: Dr. Friendly

Current Score : 4 / 87

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

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

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Question

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Total

4/87 (4.6%)

Instructions

Introduction to Statistics and Data Analysis (AP® Edition), 6th Edition, by Peck, Short, and Olsen, published by Cengage Learning, lowers the reading level from the previous edition and significantly increases homework scaffolding for difficulty level. In order to get students thinking statistically, this text stresses interpretation and communication of statistical information through hands-on, activity based learning using real data. Written in compliance with the GAISE college report and employing techniques based on modern research into student learning, this text places emphasis on how concepts apply to students and the world around them, then gets into methods using data analysis tools or hand-calculations where necessary. This 6th Edition contains new sections on randomization-based inference: bootstrap methods for simulation-based confidence intervals and randomization tests of hypotheses. The AP® edition includes exam tips throughout the text along with sections designated to address common errors on the AP® exam. The WebAssign component for this text engages students with an interactive eBook and several other resources.

Question 1 shows multiple choice questions to categorize variable types.

Question 2 asks students to enter the test statistic and p-value then answer multiple choice questions about the conclusion. Students can use SALT to answer this question.

Question 3 asks students to numerically enter the regression line and some predicted values.

Question 4 is an example of a Statistical Lab. These activities support SPSS, Minitab, R, JMP, Excel, and TI 83/84 or TI-Inspire calculators.

Question 5 and 6 ask students to numerically enter statistics then answer MC questions. Students can use SALT to answer these questions.

Question 7 is a Simulation Question utilizing the JMP Applet.

Question 8 is a Concept Question where students are asked to provide a short answer to a prompt, then answer multiple choice question about the sample prompt, then reflect on their original answer.

Question 9 walks the student through creation of a simple sampling distribution and graph.

Question 10 has students create a confidence interval at two levels and compare widths. Students can use SALT to answer this question.

Question 11 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 of display.

Question 12 highlights Milestone 1, the first step in presenting and tracking Project Milestones for a statistical research project.

Question 13 is an AP® practice question. 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. 4/5 points | Previous Answers PODStat6HS 1.E.012. My Notes

2. –/4 points PODStat6HS 10.E.030.MI.S. My Notes

In a survey of 1,000 women aged 22 to 35 who work full time, 545 indicated that they would be willing to give up some personal time in order to make more money. The sample was selected in a way that was designed to produce a sample that was representative of women in the targeted age group.

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

(a)

Do the sample data provide convincing evidence that the majority of women aged 22 to 35 who work full-time would be willing to give up some personal time for more money? Test the relevant hypotheses using

α = 0.01.

Find the test statistic and P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)

z	=
P-value	=

State your conclusion.

Reject H₀. We have convincing evidence that a majority of women aged 22 to 35 who work full time would be willing to give up some personal time for more money. Fail to reject H₀. We have convincing evidence that a majority of women aged 22 to 35 who work full time would be willing to give up some personal time for more money. Reject H₀. We do not have convincing evidence that a majority of women aged 22 to 35 who work full time would be willing to give up some personal time for more money. Fail to reject H₀. We do not have convincing evidence that a majority of women aged 22 to 35 who work full time would be willing to give up some personal time for more money.

(b)

Would it be reasonable to generalize the conclusion from part (a) to all working women? Explain why or why not.

Yes, the survey included all working adults aged 22 to 35. No, the sample size was too small. Yes, the sample size was large enough. Yes, the survey included all women. No, the survey only included women aged 22 to 35.

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3. –/4 points PODStat6HS 13.E.002. My Notes

Let x be the size of a house (in square feet) and y be the amount of natural gas used (therms) during a specified period. Suppose that for a particular community, x and y are related according to the simple linear regression model with the following values.

β = slope of population regression line = 0.019
α = y intercept of population regression line
= −7

Houses in this community range in size from 1,000 to 3,000 square feet.

(a)

What is the mean value of gas usage (in therms) for houses with 2,100 sq. ft. of space?

therms

(b)

What is the average change in usage (in therms) associated with a 1 sq. ft. increase in size?

therms

(c)

What is the average change in usage (in therms) associated with a 100 sq. ft. increase in size?

therms

(d)

Should the model be used to predict mean usage for a 500 sq. ft. house? Why or why not?

No. The model predicts a negative mean usage for this size of house. Yes. The model can be used to predict mean usage for any sized house regardless of the sample the model is based on. No. The size of this house is too big and lies outside the range of the sample that the model is based on. Yes. The size of this house lies inside the range of the sample that the model is based on. No. The size of this house is too small and lies outside the range of the sample that the model is based on.

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4. –/9 points PODStat6HS 3.Lab.001.Excel. My Notes

Statistical Lab

Background

The National Institutes of Health conducts ongoing surveys of US adults called the Health Information National Trends Survey (hereafter abbreviated HINTS).

From the National Institutes of Health: "The HINTS data collection program was created to monitor changes in the rapidly evolving field of health communication. Survey researchers are using the data to understand how adults 18 years and older use different communication channels, including the Internet, to obtain vital health information for themselves and their loved ones...."

A doctor and a patient are talking in an examination room.

The most recent round of data collection occurred over the course of September 2013–November, 2013 in HINTS 4 Cycle 3. In this lab, you will be using a subset of the HINTS 4 Cycle 3 data to practice creating effective and informative graphical representations of data, which may include histograms and pie charts.
About the Data
For this lab, you need to download the hintsdata.csv dataset. The variables you will be working with are as follows.
- Age—assume each person's age was rounded to the nearest year; for example, a person in the age
  range [19.5, 20.5)
  would have a reported age of 20, and a person in the
  range [20.5, 21.5)
  would have a reported age of 21, and so on.
- Gender—the gender of the respondent; categories include 1 = Male and 2 = Female.
- GeneralHealth—how the respondent rates their overall health; categories include 1 = Excellent, 2 = Very Good, 3 = Good, 4 = Fair, 5 = Poor.
General Notes
A few important aspects of creating effective graphical displays of data include the following.
1. labeling your graphs with descriptive titles
2. ensuring that the x- and y-axes have appropriate labels
3. setting the axes to meaningful and/or useful scales
Your graphs are expected to have these three characteristics.
Tech Guide

You will need to use the Excel Tech Guide.
Lab Questions

Create a histogram of the variable Age with class intervals 10 years wide. (Submit a file with a maximum size of 1 MB.)

This answer has not been graded yet.

Describe the shape of the above histogram.

The distribution is , centered near , with variability.

Create a pie chart of the variable GeneralHealth. (Submit a file with a maximum size of 1 MB.)

This answer has not been graded yet.

Describe how the majority of people in the survey feel about their general state of health.

The majority of people in the survey feel that their general state of health is .

You wish to determine if the age of the respondents who perceive themselves to be in good health differs from the age of the respondents who perceive themselves to be in poor health. Do this by creating two histograms. For the first histogram, plot the variable Age using only the data from respondents who rate their overall health as Excellent, Very Good, or Good. For the second histogram, plot the variable Age using only the data from respondents who rate their overall health as Fair or Poor. Make sure to label your histograms and make sure that they have the same limits for the x-axis, y-axis, and class intervals, so that they can be directly compared. (Submit a file with a maximum size of 1 MB.)

This answer has not been graded yet.

Briefly discuss.

This answer has not been graded yet.

Compare how men and women rate their general state of health using a comparative chart. Using your chart, briefly compare and contrast how men and women rate their general state of health.

This answer has not been graded yet.

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5. –/4 points PODStat6HS 4.E.017.MI.S. My Notes

The following data are costs (in cents) per ounce for nine different brands of sliced Swiss cheese.

28 63 37 43 70 84 48 54 49

(a)

Calculate the variance for this data set. (Round your answer to four decimal places.)

Calculate the standard deviation for this data set. (Round your answer to four decimal places.)

(b)

If a very expensive cheese with a cost per slice of 150 cents was added to the data set, how would the values of the mean and standard deviation change?

The addition of the very expensive cheese would the value of the mean and the value of the standard deviation.

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6. –/5 points PODStat6HS 4.E.038.S. My Notes

Fiber content (in grams per serving) for 18 high fiber cereals are shown below.

Fiber Content
6	11	11	6	8	6	12	12	8
13	11	8	12	6	14	6	8	8

(a)

Find the median, quartiles, and interquartile range for the fiber content data set.

median = lower quartile = upper quartile = interquartile range =

(b)

Explain why the minimum value for the fiber content data set and the lower quartile for the fiber content data set are equal.

The bottom quarter of the data values are all the same value. The upper quarter of the data values are all the same value. The minimum value and the lower quartile are always the same value.

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7. –/5 points PODStat6HS 4.JMP.008. My Notes

The population (in thousands) of 52 cities was collected and the graph and summary statistics of this data are given in the JMP Applet.

Cities' populations

CITY	POP
ALBANY	846
ALBUQUERQUE	486
ATLANTA	2657
ATLANTIC CITY	303
BALTIMORE	2303
BOSTON	2842
BURLINGTON	127
CHARLESTON	502
CHARLOTTE	1091
CHEYENNE	76
CHICAGO	6199
CINCINNATI	1438
CLEVELAND	1851

CITY	POP
DENVER	1645
DES MOINES	385
DETROIT	4362
DUBUQUE	91
GALVESTON-T.C.	211
HARRISBURG	584
HARTFORD	748
HOUSTON	3228
HUNTINGTON	323
INDIANAPOLIS	1229
JACKSON	396
JACKSONVILLE	878
LOS ANGELES	8505

CITY	POP
LOUISVILLE	967
MADISON	347
MIAMI	1791
MILWAUKEE	1389
MINNEAPOLIS	2336
MOBILE	438
MONTGOMERY	297
NASHVILLE	956
NEW ORLEANS	1321
NEW YORK	8529
NORFOLK	1346
OKLAHOMA CITY	975
OMAHA	616

CITY	POP
PHILADELPHIA	4866
PHOENIX	1960
PORTLAND	210
PORTLAND	1168
RALEIGH	665
SALT LAKE CITY	1055
SAN FRANCISCO	1590
SEATTLE	1796
SPOKANE	355
ST. LOUIS	2458
WASHINGTON	3646
WICHITA	475
WILMINGTON	559

JMP Applet

Click here to access the JMP applet in a new window.
(a)

Determine the interquartile range.

thousand

What percent of data is represented by this range?

%
(b)

What value separates the upper 75% of data from the lower 25%?
(c)

Which cities are considered upper outliers according to the IQR method? (Select all that apply.)

Chicago Washington Detroit New York Philadelphia Los Angeles Houston none of the above
(d)

Which cities are considered lower outliers according to the IQR method? (Select all that apply.)

Dubuque Burlington Cheyenne Portland none of the above

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8. –/3 points PODStat6HS 8.CQ.002. My Notes

This question is related to sampling distribution.

If a normal population has a standard deviation σ = 38.6, what is the standard error of the mean (standard deviation of the x's) if samples of size 16 are selected? What is the standard error if samples of size 49 are taken? What is the standard error if samples of size 100 are taken? (Round your answers to two decimal places.)

Regardless of sample size, why is the standard deviation of the x's always smaller than the standard deviation of the population?

This answer has not been graded yet.

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9. –/15 points PODStat6HS 8.E.007. My Notes

Consider the following population: {2, 3, 4, 5}. For this population the mean is

μ =

2 + 3 + 4 + 5

= 3.5

Suppose that a random sample of size 2 is to be selected without replacement from this population. There are 12 possible samples (provided that the order in which observations are selected is taken into account).

2, 3	2, 4	2, 5	3, 2	3, 4	3, 5
4, 2	4, 3	4, 5	5, 2	5, 3	5, 4

(a)

Calculate the sample mean for each of the 12 possible samples.

Sample	Sample Mean
2, 3
2, 4
2, 5
3, 2
3, 4
3, 5
4, 2
4, 3
4, 5
5, 2
5, 3
5, 4

(b)

Use the sample means to construct the sampling distribution of x. Display the sampling distribution as a density histogram.

A histogram has 5 rectangles of equal width along a horizontal axis labeled "Sample Mean" which ranges from about 2.25 to 5. The vertical axis is labeled "Density" and ranges from 0 to about 0.9. The approximate endpoints of each class interval and approximate height of each rectangle are as follows.

between 2.25 and 2.75: 0.364

between 2.75 and 3.25: 0.364

between 3.25 and 3.75: 0.545

between 3.75 and 4.25: 0.364

between 4.25 and 4.75: 0.364

(c)

Suppose that a random sample of size 2 is to be selected, but this time sampling will be done with replacement. Using a method similar to that of part (a), construct the sampling distribution of x. (Hint: There are 16 different possible samples in this case.)

A histogram has 5 rectangles of equal width along a horizontal axis labeled "Sample Mean" which ranges from about 1.75 to 5.5. The vertical axis is labeled "Density" and ranges from 0 to about 0.8. The approximate endpoints of each class interval and approximate height of each rectangle are as follows.

between 2.25 and 2.75: 0.333

between 2.75 and 3.25: 0.333

between 3.25 and 3.75: 0.667

between 3.75 and 4.25: 0.333

between 4.25 and 4.75: 0.333

A histogram has 7 rectangles of equal width along a horizontal axis labeled "Sample Mean" which ranges from about 1.75 to 5.5. The vertical axis is labeled "Density" and ranges from 0 to about 0.8. The approximate endpoints of each class interval and approximate height of each rectangle are as follows.

between 1.75 and 2.25: 0.125

between 2.25 and 2.75: 0.250

between 2.75 and 3.25: 0.375

between 3.25 and 3.75: 0.500

between 3.75 and 4.25: 0.375

between 4.25 and 4.75: 0.250

between 4.75 and 5.25: 0.125

(d)

In what ways are the two sampling distributions of parts (b) and (c) similar? In what ways are they different? (Select all that apply.)

Their means are different. They are both symmetrical. One distribution is not symmetrical. They both cover the same range. One distribution covers a larger range. Their means are equal.

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10. –/10 points PODStat6HS 9.E.021.S. My Notes

11. –/4 points PODStat6HS 9.SIP.501.XP. My Notes

12. –/18 points PODStat6HS PJT.1.001. My Notes

Question Part

Points

Submissions Used

–/1

0/100

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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13. –/1 points PODStat6HS 7.AP.008. My Notes

For a normally distributed population with mean 0 and standard deviation 1.0, the population interquartile range is closest to which of the following values?

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Peck, Short & Olsen - Intro to Statistics (AP) 6/e (Homework)

Current Score : 4 / 87

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

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

Instructions

Assignment Submission

Assignment Scoring

Statistical Lab

Background

About the Data

General Notes

Tech Guide

Lab Questions

Cities' populations

JMP Applet

(a)

(b)

(c)

(d)

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