MAT 130: Beginning Statistics

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Student Name

Allied American University

Author Note

This paper was prepared for [INSERT COURSE NAME], [INSERT COURSE ASSIGNMENT] taught by [INSERT INSTRUCTOR’S NAME].

PART I: SHORT RESPONSE

Directions: Please answer each of the following questions thoroughly.

1. For each of several randomly selected years, the total number of points scored in the Super Bowl football game and the total number of new cars sold in the United States are recorded.

a. For this sample of paired data, what does r represent?

b. What does ρ represent?

c. Without doing any research or calculations, estimate the value of r.

2. What is meant by the statement that correlation does not imply causality?

3. Describe the error in the stated conclusion for each statement.

a. Given: There is a linear correlation between the number of cigarettes smoked each day and the pulse rate, so that more smoking is associated with a higher pulse rate.

Conclusion: Smoking causes an increase in the pulse rate.

b. Given: There is a linear correlation between annual personal income and years of education.

Conclusion: More education causes a person’s income to rise.

4. A jeweler at Tiffany & Company computes the value of the linear correlation coefficient for pairs of sample data consisting of Tiffany prices for gold wedding rings and the corresponding prices at a discount store. She obtains a value of r = 1 and concludes that the prices at both companies are the same. Is she correct? Why or why not?

5. Use the given data below to find the best predicted value of the response variable. Be sure to follow the prediction procedure summarized in Figure 10-5 in your textbook.

a. In a study conducted by University of Arizona researchers, the total weight (in pounds) of garbage discarded in one week and the household size were recorded for 62 households. The linear correlation coefficient is r = 0.759 and the regression equation is , where x represents the total weight of discarded garbage. The mean of the 62 garbage weights is 27.4 lb and the 62 households have a mean size of 3.71 people. What is the best predicted number of people in a household that discards 50 lb of garbage?

b. A sample of eight mother daughter pairs of subjects was obtained, and their heights (in inches) were measured. The linear correlation coefficient is 0.693 and the regression equation is , where x represents the height of the mother (based on data from the National Health Examination Survey). The mean height of the mothers is 63.1 in. and the mean height of the daughters is 63.3 in. Find the best predicted height of a daughter given that the mother has a height of 60 in.

6. Define the following terms from section 10-4:

a. Total deviation

b. Explained deviation

c. Unexplained deviation

7. Using the definitions from problem 6, define the following terms and how they relate to each other:

a. Total variation

b. Explained variation

c. Unexplained variation

d. Coefficient of determination

8. A wedding caterer randomly selects clients from the past few years and records the months in which the wedding receptions were held. The results are listed below (based on data from The Amazing Almanac). Assume that you want to test the claim that weddings occur in different months with the same frequency. Briefly describe what O and E represent, then find the values of O and E.

9. When using the data from the above exercise to conduct a hypothesis test of the claim that weddings occur in the 12 months with equal frequency, we obtain the P-value of 0.477. What does that P-value tell us about the sample data? What conclusion should be made?

10. The table below summarizes results from an experiment in which subjects were first classified as smokers or nonsmokers, then they were given a treatment, then later were again classified as smokers or nonsmokers.

a. How many subjects are included in the experiment?

b. How many subjects changed their smoking status after the treatment?

c. How many subjects appear to be unaffected by the treatment one way or the other?

d. Section 9-4 in your textbook presented procedures for data consisting of matched pairs. Why can’t we use the procedures of Section 9-4 for the analysis of the results summarized in the table?

e. Which of the following pairs of before/after results are discordant?

i. Smoke/Smoke

ii. Smoke/Don’t Smoke

iii. Don’t Smoke/Smoke

iv. Don’t Smoke/Don’t Smoke

f. Using the appropriate frequencies, find the value of the test statistic.

g. Using a 0.01 significance level, find the critical value.

h. Based on the preceding results, what do you conclude? How does the conclusion make sense in terms of the original sample results?

PART II: PROJECT

For this Module 6 Homework Assignment, please submit your response to the following:

Document your progress. Who did you interview? How many people did you interview? If you collected data, please submit it below. If not, please explain what you did to contribute to this assignment this past week.

Directions: This assignment is a course-long project whereby you will work on the project in each module. You will turn in your completed project at the end of Module 8.

Create a survey question to ask others. The following are examples or some survey questions:

1. Choose a random number between 1 and 10 inclusive.

2. What month of the year does your birthday fall on? Write the numeric value from 1 to 12.

3. How many keys are in your possession at this time?

4. How many siblings do you have?

In Module 1, you will submit your survey question to your instructor for approval. Once you are notified of its approval, you may begin conducting a survey using your question.

You will need at least 25 participants and will need to keep the following record for each person:

a. Gender

b. Age

c. Date surveyed

d. Survey response

Please also keep a count, if any, non-willing participants. For example, if you chose the first survey question, then you might have the following records:

In the Module 8 Homework Assignment, you will be asked to analyze your survey results, so please be sure to begin conducting your survey as soon as your question is approved. Try getting 5 participants a week to satisfy the required number of participants.