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Statistics, section 2, Fall 2019
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Peck et al - Intro to Stats and Data Analysis 7/e (Homework)

James Finch

Statistics, section 2, Fall 2019

Instructor: Dr. Friendly

Current Score : – / 121

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

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

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Question

Points

1	2	3	4	5	6	7	8	9	10	11	12	13
–/17	–/4	–/3	–/18	–/10	–/19	–/19	–/2	–/5	–/4	–/5	–/10	–/5

Total

–/121 (0.0%)

Instructions

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.

WebAssign provides a wide range of exercises that enable you to:

Gain student interest and encourage critical thinking (#1-4: Select Your Scenario, Stats in Practice, and Project Milestone Exercises)
Explore, visualize, and analyze real data with technology (#5-7: SALT, Stats Lab, and JMP Simulation Exercises)
Develop conceptual understanding (#8-13: Intro Stats Readiness Bootcamp, Interpreting and Communicating the Results of Statistical Analysis, and Statistics Question Collection Exercises)

Category 1: Gain student interest and encourage critical thinking

1. SELECT YOUR SCENARIO questions engage students by letting them pick the topic (from a choice of 3) that most interests them.

2. STATS IN PRACTICE Video questions demonstrate the relevance of topics in a real-world context.

3. CONCEPT VIDEO questions are 7-10 minutes in length and are designed to help students with big picture understanding of statistics by discussing a concept followed by two to three comprehension questions.

4. PROJECT MILESTONES enable students to complete a research project across four steps: Research Design, Gather Data, Analyze Data and Present Results

Category 2: Explore, visualize and analyze real data with technology

5. THE STATISTICAL ANALYSIS & LEARNING TOOL (SALT) enables Intro Stats students to analyze and visualize data and think statistically without getting bogged down in complex computations

6-7. STATS LABS enable students to get hands-on and analyze real data

Category 3: Develop conceptual understanding

8. The INTRO STATS READINESS BOOTCAMP assesses prerequisite skills and provides tutorial support to prepare students for success (This is one question from the prebuilt bootcamp).

9-12. INTERPRETING AND COMMUNICATING THE RESULTS OF STATISTICAL ANALYSIS sections emphasize the importance of being able to interpret statistical output and communicate its meaning to non-statisticians.

13. STATISTICS QUESTION COLLECTION is a free additional resource that includes real-world data sets, 500+ relevant examples and 1500+ assessments across a variety of major-specific interests.

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. –/17 points PODStat7 7.5.SYS.001.S. My Notes

This exercise will gain student interest and encourage critical thinking.
Select Your Scenario questions provide students with 3 different contexts to choose from. Students select the scenario most relevant to them, and then solve the problem which requires them to answer questions demonstrating knowledge of a learning objective.

Instructions

Select Your Scenario:

This problem contains data for 3 different scenarios: Social Media, Health Care, and Criminal Justice.

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.

Social Media

Would you post a photo or video about your vacation on social media? It has been reported that 87% of social media users would post about a positive travel experience. For a random sample of 61 people who recently were on vacation, compute probabilities for the following situations.

State the single outcome that is most likely to occur along with its probability.
The probability that x is at most 50.
The probability that x is at least 54.
The probability that x is more than 47 and less than 58.
The probability that x is more than 55.
The probability of no successes in the trials.
The probability that all n trials results in a success.

Health Care

Suppose 44 patients arrive at a hospital emergency department on any given day. Recent data indicate that approximately 19% of these patients are admitted for inpatient care. We will consider these 44 patients to be a representative sample of people who are served by this hospital and compute probabilities for the following situations.

State the single outcome that is most likely to occur along with its probability.
The probability that x is at most 4.
The probability that x is at least 10.
The probability that x is more than 3 and less than 14.
The probability that x is more than 15.
The probability of no successes in the trials.
The probability that all n trials results in a success.

Criminal Justice

According to an organization focused on collecting criminal justice statistics, of the property crimes that were reported to the police in 2015, 18% were cleared through arrest, charging, and referral of the suspect for prosecution. Suppose 12 property crimes were reported in a town last year and that these crimes are independent, compute probabilities for the following situations.

State the single outcome that is most likely to occur along with its probability.
The probability that x is at most 2.
The probability that x is at least 4.
The probability that x is more than 1 and less than 8.
The probability that x is more than 5.
The probability of no successes in the trials.
The probability that all n trials results in a success.

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

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2. –/4 points PODStat7 9.CE.001.SIP. My Notes

3. –/3 points PODStat7 1.CE.001.CV. My Notes

4. –/18 points PODStat7 PJT.1.001. My Notes

Question Part

Points

Submissions Used

–/1

0/100

Total

–/18

This exercise will gain student interest and encourage critical thinking.
Project Milestones allow instructors to assign and track long-term projects that enable students to design and conduct their own statistical research to help solidify big picture understanding.

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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5. –/10 points PODStat7 13.1.010.S. My Notes

This exercise will explore, visualize, and analyze real data with technology.
Statistical Analysis and Learning Tool questions in WebAssign include an embedded data analysis tool that helps your students easily visualize and analyze data.

The ability to jump helps salamanders move quickly to avoid predators. A paper investigated jumping behavior of 10 species of salamanders and reported the following data on bend angle (the bend [in degrees] in the salamander body, with a larger number reflecting more extreme bending) and the jump takeoff velocity (in meters per second).

Bend Angle	Takeoff Velocity
36.6	0.6
55.1	0.7
46.6	0.7
50.3	0.7
69.9	0.9
71.1	1.0
67.5	1.1
48.0	0.7
61.7	0.9
52.5	0.9

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

A simple linear regression model can be used to describe the relationship between x = Bend angle (in degrees) and y = Takeoff velocity (in m/s).

(a)

What is the equation of the estimated regression line? (Round your numerical values to four decimal places.)

ŷ =

(b)

What is the estimated average increase in takeoff velocity (in m/s) associated with a 1 degree change in bend angle? (Round your answer to four decimal places.)

m/s

(c)

What would you predict takeoff velocity (in m/s) to be for a salamander who jumps with a bend angle of 50 degrees? (Round your answer to three decimal places.)

m/s

(d)

Should you use this regression model to predict takeoff velocity for a salamander who jumps with a bend angle of 90 degrees? Explain.

This model be used to predict takeoff velocity for a salamander who jumps with a bend angle of 90 degrees because that value is the range of bend angles that were used to develop the model.

(e)

Calculate the value of r². (Round your answer to four decimal places.)

r² =

Interpret this value.

This value of r² tells us what proportion of the variability in takeoff velocity is random. This value of r² tells us what proportion of the variability in takeoff velocity can be explained by the linear relationship between takeoff velocity and bend angle. This value of r² tells us what proportion of the values of takeoff velocity and bend angle will fall on the estimated regression line. This value of r² tells us what proportion of the variability in takeoff velocity cannot be explained by the linear relationship between takeoff velocity and bend angle. This value of r² tells us what proportion of the values of takeoff velocity and bend angle will not fall on the estimated regression line.

(f)

Calculate the value of

s_e.

(Round your answer to five decimal places.)

s_e =

Interpret this value.

This value of s_e tells us the typical amount by which a value the valued predicted by the least squares regression line.

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6. –/19 points PODStat7 7.5.ST.001.S. My Notes

Question Part

Points

Submissions Used

–/1

0/100

Total

–/19

This exercise will explore, visualize, and analyze real data with technology.
Students perform real statistical analysis in class or online with pre-built, chapter-specific Stats Labs using the data analysis tool of your choice (R, JMP, Minitab, SPSS, Excel or Graphing Calculator) to analyze a real dataset—facilitating whole-picture learning.

The following exercise will guide you through how to use SALT to calculate binomial probabilities.

In the era of social networks and digital marketing, customers' voices have become increasingly authoritative. According to a recent survey, 33% of diners chose to dine at a restaurant based on the information from a peer review site. We will consider a random sample of 24 people who go out to eat and use the Binomial Probability Distribution to model the behavior of the random variable described in this scenario. Before we compute any probabilities, let's see how this scenario meets the criteria of a Binomial Experiment.

A Binomial Experiment consist of a sequence of trials with the following conditions:

There are a fixed number of trials.

For this scenario, we will survey a random sample of 24 people. Thus we have a fixed number of trials in this scenario and the number of trials is defined to be n = .
Each trial can result in one of only two possible outcomes, labeled success and failure.

There are exactly two outcomes for each diner in our random sample: the diner chose where to eat based on the information from a peer review site or they chose based on some other criteria. We will count the number of diners who chose a restaurant based on the information from a peer review site, so this outcome will be labeled a success. Any diner who used some other criteria will be labeled a failure. Thus, only two outcomes possible for each trial and are labeled success or failure.
Outcomes of different trials are independent.

Since we have a random sample, we can assume that these people are strangers to each other. Thus, the outcomes of the 24 trials independent.
The probability that a trial results in a success is the same for each trial.

The survey reported 33% of diners chose to dine at a restaurant based on the information from a peer review site. This rate change at each trial so we can define the probability of success to be p = (entered as a decimal, not a percent) and the probability of failure to be
1 − p.

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7. –/19 points PODStat7 10.Lab.002.Excel. My Notes

8. –/2 points WAStatsBootcamp1 4.2.001. My Notes

This exercise will develop conceptual understanding.
This exercise helps your student develop conceptual understanding. The exercise requires the student to interpret and communicate the results of statistical analysis, emphasizing the importance of being able to interpret statistical output and communicate its meaning to non-statisticians.

For the line, identify the slope

(b)

and identify the y-intercept

(a).

y = 0.838 + 0.16x

slope b = y-intercept a =

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9. –/5 points PODStat7 10.3.039.S. My Notes

This exercise will develop conceptual understanding.
This exercise helps your student develop conceptual understanding. The exercise requires the student to interpret and communicate the results of statistical analysis, emphasizing the importance of being able to interpret statistical output and communicate its meaning to non-statisticians.

The article titled "7% of Americans Don't Use the Internet. Who Are They?" describes a study conducted by the Pew Research Center.†Source: Pew Research Center (April 2, 2021) Suppose that the title of this article is based on a representative sample of 700 adult Americans. Does this support the claim that the proportion of adult Americans who do not use the Internet is less than 0.10 (10%)? Test the relevant hypotheses using a significance level of 0.05.

State the appropriate null and alternative hypotheses. (Let p be the population proportion of adult Americans who do not use the internet. Enter != for ≠ as needed.)

H₀:

H_a:

Find the test statistic. (Round your answer to two decimal places.)

Use technology to find the P-value. (Round your answer to four decimal places.)

P-value =

State the conclusion in the problem context.

Reject H₀. We do not have convincing evidence that the proportion of adult Americans who do not use the Internet is less than 10%. Fail to reject H₀. We have convincing evidence that the proportion of adult Americans who do not use the Internet is less than 10%. Fail to reject H₀. We do not have convincing evidence that the proportion of adult Americans who do not use the Internet is less than 10%. Reject H₀. We have convincing evidence that the proportion of adult Americans who do not use the Internet is less than 10%.

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10. –/4 points PODStat7 4.2.017.S.MI. My Notes

This exercise will develop conceptual understanding.
This exercise helps your student develop conceptual understanding. The exercise requires the student to interpret and communicate the results of statistical analysis, emphasizing the importance of being able to interpret statistical output and communicate its meaning to non-statisticians.

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

27 64 36 41 70 84 47 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 ounce of $1.50 (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.

Need Help?

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11. –/5 points PODStat7 4.3.038.S. My Notes

This exercise will develop conceptual understanding.
This exercise helps your student develop conceptual understanding. The exercise requires the student to interpret and communicate the results of statistical analysis, emphasizing the importance of being able to interpret statistical output and communicate its meaning to non-statisticians.

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

Fiber Content
6	10	10	6	9	6	12	12	9
13	10	9	12	6	14	6	9	9

(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 upper quarter of the data values are all the same value. The bottom 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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12. –/10 points PODStat7 9.2.021.S. My Notes

13. –/5 points StatsQC1 17.2C.008.CH.S. My Notes

This exercise will develop conceptual understanding.
This exercise helps your student develop conceptual understanding. The exercise requires the student to interpret and communicate the results of statistical analysis, emphasizing the importance of being able to interpret statistical output and communicate its meaning to non-statisticians.

Like any seeds, watermelon seeds lose their viability over time. If they've been left sitting for years, it's possible that only a small proportion of the seeds may sprout when planted. If they have been stored in a cool, dark, dry location, they have a better chance of sprouting. Drake has a large quantity of old watermelon seeds he's been saving, and now wants to know how many of them may still be able to sprout.

He randomly selects 100 seeds from the set, places them between damp paper towels, and puts them in a plastic baggie in a warm spot on the counter. He finds that 58 out of the 100 seeds do sprout. Does this provide good evidence that over half of all of the seeds will sprout?

(a)

What proportion of Drake's tested seeds actually sprouted?

p̂ =

(b)

State the appropriate null and alternative hypotheses.

H₀:

p 0.5

H_a:

p 0.5

(c)

What is the value of z, the test statistic, for this test? (Round your answer to two decimal places.)

z =

(d)

At a significance level of 0.05, what conclusion would you write about whether Drake has evidence to support that more than half of all of his seeds will sprout?

Because the P-value is greater than our alpha level of 0.05, we reject the null hypothesis and conclude that there's enough evidence to state that more than half of all of the seeds will sprout. Because the P-value is greater than our alpha level of 0.05, we fail to reject the null hypothesis and conclude that there's not enough evidence to state whether more than half of all of the seeds will sprout. Because the P-value is less than our alpha level of 0.05, we fail to reject the null hypothesis and conclude that there's not enough evidence to state whether more than half of all of the seeds will sprout. Because the P-value is less than our alpha level of 0.05, we reject the null hypothesis and conclude that there's enough evidence to state that more than half of all of the seeds will sprout.

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Home My Assignments Extension Request

Peck et al - Intro to Stats and Data Analysis 7/e (Homework)

Current Score : – / 121

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

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

Instructions

Assignment Submission

Assignment Scoring

Stats in Practice: Estimation

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

Statistical Lab

Background

Guidelines

About the Data

Tech Guide

Lab Questions

References