Computer Oriented Approach to Statistics – Assignment 5

Assignment 5 consists of a theory component (5A, worth 80%) and a computer component (5B, worth 20%).
The grades allocated are summarized below.

Assignment	Grade weight (%)
Assignment 5A. Theory	80
Assignment 5B. Computer	20
Total marks	100

You must submit Assignment 5A and Assignment 5B together as PDFs, through the appropriate drop box on the course home page. Submit:

1. One PDF solution file (file) entitled Assignment5A containing all your answers to Assignment 5A, presented in the proper order. Your name and student ID number must be at the top of the first page of your solution file.

and

• One PDF solution file (file) entitled Assignment5B containing all your answers to Assignment 5B, presented in the proper order.

We suggest that you print the Assignment 5 questions, so that you can conveniently review the questions with their solutions when you prepare for your exams.

Assignment 5A. Theory Component

Show your work for this component. Where relevant and unless otherwise instructed, keep your calculations and your final answer to at least four decimals. For any test of hypothesis questions, show all steps in detail and provide a conclusion in terms of the context of the question.

Problem 1. Salaries (23 marks)

A study was conducted to determine if the salaries of the professors from two neighbouring universities were equal. A sample of 20 professors from each university was randomly selected. The mean from the first university was $109,100 with a population standard deviation of $2300. The mean from the second university was $110,500 with a population standard deviation of $2100. Assume that the distribution of professor salaries, at both universities, are approximately normally distributed. Level of significance = 0.05.

1. Using the critical value approach test the claim that the salaries from both universities are equal. Include all key steps of the test. [10 marks]
2. Use the four-step P-value approach and test the claim that the salaries from both universities are equal. [10 marks]
3. Are the conditions met for using this test? [3 marks]

Problem 2. Flexibility (12 marks)

Are women more flexible than men? To answer this question, a physical therapist measured the flexibility of 15 randomly selected women and 20 randomly selected men by determining the number of inches subjects could reach while sitting on the floor with their legs straight out and back perpendicular to the ground. The more flexible an individual is, the more they can reach from the seated position. The physical therapist obtained the following data:

Gender	Sample Size	Mean ( in inches)	SD (in inches)
Women	15	20.86	2.11
Men	20	18.43	3.16

Assume that both population distributions are approximately normal and that the population variances are NOT equal.

1. Is the sampling dependent or independent in this study? Justify your answer. [2 marks]
2. Test the hypothesis at α = 0.05. Using the critical value approach, include all key steps of test of hypothesis. [10 marks]

Problem 3. Customer waiting times (10 marks)

Bank A claims that the waiting time for its customers is less than its competitor Bank B’s customers. A researcher collected data on the wait time for customers from both banks. Test the claim. Assume the samples are random and independent, and the populations are normally distributed. Also, assume that the unknown population variances are equal. Test the claim at 0.01 level of significance.

Bank A	Bank B
= 15  = 5.3 minutes  = 1.1 minutes	= 16  = 5.6 minutes  = 1.0 minutes

Is there sufficient evidence to believe that the wait time for Bank A is less than for Bank B? Include all key steps of test of hypothesis, using the critical value approach. [10 marks]

Problem 4. Cholesterol levels (12 marks)

A pharmaceutical company introduced a new drug that would reduce cholesterol levels. A researcher selected 10 cholesterol patients and tested them for their cholesterol level. The subjects were then placed on the new drug for a period of 6 months, and the cholesterol level reading was taken again. Both the results are given below. Assume the samples are random and dependent, and the populations are normally distributed. Use 0.01 level of significance and test whether there is evidence of reduced cholesterol level.

Subject	A	B	C	D	E	F	G	H	I	J
Before	196	224	201	196	176	259	265	193	240	268
After	181	219	209	176	170	229	255	190	240	250

1. Is the sampling dependent or independent in this study? Justify your answer. [2 marks]
2. Use the critical value approach, test whether there is evidence of reduced cholesterol level. Include all key steps of the test. [10 marks]

Problem 5. Health care (23 marks)

In a random survey of 500 doctors that practice specialized medicine, 20% felt that health care should be privatized in Canada. In a random sample of 800 family physicians, 30% felt that the health care should be privatized in Canada. Is there any difference in the two proportions? Use α = 0.10.

1. Are the conditions met for using a z test to test this claim? [3 marks]
2. Use the four-step P-value approach and test the claim described here. [10 marks]
3. Using the critical value approach, test the hypothesis for the claim described here. Include all key steps of the test of hypothesis. [10 marks]

Assignment 5B. Computer Component

Show your work for this component. Where relevant and unless otherwise instructed, keep your calculations and your final answer to at least four decimals.

Do NOT round off the results you get in StatCrunch.

Problem 1. Basketball

The scoring averages (points per game) of 10 professional basketball players for their first and second seasons are displayed in the StatCrunch data file BBall1.txt, available in the StatCrunch Math 216 Group folder. At a 10% level of significance, use StatCrunch to test the coach’s claim that the scoring averages have changed from the first season to the second season.

1. Open the StatCrunch file BBall1.txt. Use the four-step P-value approach to test whether the average points scored per game have changed from the first season to the second season, at a 10% level of significance. Copy and paste the Hypothesis Test Results window from StatCrunch to the Word file Assignment5B under the subheading Problem 1a under Step 2 of the test. [2 marks]
2. What key assumption was made when you tested the coach’s claim in Problem 1a? Type your answer in the Word file Assignment5B under the subheading Problem1b. [1 mark]
3. At the 5% level of significance, use the four-step P-value approach to test the hypothesis that the sample of differences comes from a population of differences that is normally distributed. Copy and paste the Hypothesis Test Results window from StatCrunch to the Word file Assignment5B under the subheading Problem1c under Step 2 of the test.[1 mark]

Problem 2. Teaching science

Two teaching methods and their effects on science test scores are under review. One group of students is taught in traditional lab sessions. A second group is taught using new interactive simulation software. The test scores of each group are in the StatCrunch data file Science1.txt available in the StatCrunch Math 216 group file. At a 5% level of significance, conduct a hypothesis test to see if the mean test scores under the new interactive simulation method exceed the mean test scores under the traditional lab method. Assume that both samples come from populations with equal variances.

1. Open the StatCrunch file Science1.txt. Use the four-step P-value approach to test whether the mean test scores under the new interactive simulation method exceed the mean test scores under the traditional lab method at a 5% level of significance. Assume equal population variances when conducting the test (i.e., select the pooled variance option). Copy and paste the Hypothesis Test Results window from StatCrunch to the Word file Assignment5B under the subheading Problem 2a under Step 2 of the test.
   [2 marks]
2. What assumptions did you make in conducting the hypothesis test in 2a? Type your answer in the Word file Assignment5B under the subheading Problem2b. [1 mark]
3. Conduct the appropriate hypothesis test,at alpha = 0.05, to determine if the each of the two samples of test scores comes from a normal population. Use the four-step P-value approach.Copy and paste the Hypothesis Test Results window from StatCrunch to the Word file Assignment5B under the subheading Problem2c under Step 2 of the test. [1 marks]
4. Conduct the appropriate hypothesis test, at alpha = 0.05, to determine if each of the two samples of test scores comes from populations with equal variances. Use the four-step P-value approach.Copy and paste the Hypothesis Test Results window from StatCrunch to the Word file Assignment5B under the subheading Problem2d under Step 2 of the test. [1 mark]
5. Referring to Problem 2a, use StatCrunch to construct two separate 95% confidence intervals: one interval based on the sample of test scores from the traditional lab method curriculum, and a second interval based on the sample of test scores from the new interactive simulation method. Copy and paste both confidence intervals from StatCrunch to the Word file Assignment5B under the subheading Problem2e.[1 mark]
6. Do the two confidence intervals created support your hypothesis test conclusion in Problem 2a? Type your explanation to the Word file Assignment5B under the subheading Problem2f. [1 mark]

Problem 3. Drivers

In a survey of 400 drivers from eastern Canada, 380 drivers reported that they always wear their seat belts. In a survey of 350 drivers from western Canada, 300 drivers reported that they always wear their seat belts. At the 1% level of significance, can you support the claim that the proportion of eastern Canadian drivers who always wear their seat belts exceeds the proportion of western Canadian drivers who always wear their seat belts? Use the four-step P-value approach. Copy and paste the Hypothesis Test Results window from StatCrunch to the Word file Assignment5B under the subheading Problem3 under Step 2 of the test.[2 marks]

Problem 4. Zoeys: Questionnaire

The manager of Zoeys, a fast food outlet, distributed the survey questionnaire (Figure1) to its regular customers. Twenty-five regular customers responded to this survey, and their responses are stored in the StatCrunch file Zoeys available in the Math 216 group folder on StatCrunch.

Figure 1: Zoey’s Questionnaire
For questions 1-4, please select the responses that apply to you. For questions 5-8, please write the number that applies.	Variable	Text Code
1. Please indicate your gender.	Gender
female		1
male		2
2. Please indicate your level of satisfaction with your last visit to Zoeys.	Satisfy	Code
very satisfied		1
satisfied		2
less than satisfied		3
3. Do you frequently bring children to Zoeys?	Child	Code
yes		1
no		2
4. How often do you use Zoey’s discount coupons?	Coupon	Code
frequently		1
occasionally		2
never		3
5. On a typical visit, please estimate the amount that you spend at Zoeys.	Spend	$ _______
6. How many times per month do you typically visit Zoeys?	Visits	_______
7. Please indicate your monthly family income before taxes.	Income	$ _______
8. Please indicate your age.	Age	_______

1. Open the StatCrunch data file Zoeys. At a 5% level of significance, test the hypothesis that the population mean number of visits per month made by customers who frequently bring children to Zoeys exceeds the population mean number of visits per month made by customers who do not frequently bring children to Zoeys. Use the four-step P-value approach. Copy and paste the Hypothesis Test Results window from StatCrunch to the Word file Assignment5B under the subheading Problem 4a under Step 2 of the test. Use the pooled variance option when conducting this test. [2 marks]
2. What assumptions did you make in conducting the hypothesis test in 4a? Type your answer in the Word file Assignment5B under the subheading Problem4b. [1 mark]
3. Conduct the appropriate hypothesis test, at alpha = 0.05, to determine if each of the two subset samples, number of visits made by the customers who frequently bring children and number of visits made by the customers who do not frequently bring children, comes from populations with equal variances. Use the four-step P-value approach.Copy and paste the Hypothesis Test Results window from StatCrunch to the Word file Assignment5B under the subheading Problem4c under Step 2 of the test.[1 mark]
4. Conduct the appropriate hypothesis test to determine if each of the two subset samples, number of visits made by the customers who frequently bring children and number of visits made by the customers who do not frequently bring children, comes from a normal population. Use the four-step P-value approach.Copy and paste the Hypothesis Test Results window from StatCrunch to the Word file Assignment5B under the subheading Problem4d under Step 2 of the test. [1 mark]

Problem 5. Zoeys: Satisfaction

For the following problem, refer to Zoey’s questionnaire (see Problem 4). With the StatCrunch data file Zoey open, use the four-step P-value approach to test whether the population proportion of Zoeys customers who experienced a very satisfied level of satisfaction is higher for those who frequently bring children to Zoeys, compared to those who do not frequently bring children, with a level of significance of 5%. Hint: Select the Column Variable Recode(Satisfy) with Success being VSat. Copy and paste the Hypothesis Test Results window from StatCrunch to the Word file Assignment5B under the subheading Problem5 under Step 2 of the test.
[2 marks]