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Exam 10: Inference About Means and Proportions With Two Populations

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Question 51

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A potential investor conducted a 49 day survey in two theaters in order to determine the difference between the average daily attendance at North Mall and South Mall Theaters. The North Mall Theater averaged 720 patrons per day with a variance of 100; while the South Mall Theater averaged 700 patrons per day with a variance of 96. Develop an interval estimate for the difference between the average daily attendance at the two theaters. Use a confidence coefficient of 0.95.

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16.03 to 2...

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Question 52

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Exhibit 10-10 The results of a recent poll on the preference of shoppers regarding two products are shown below. -Refer to Exhibit 10-10. The standard error of is

A) 52
B) 0.044
C) 0.0225
D) 100

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Question 53

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To construct an interval estimate for the difference between the means of two populations when the standard deviations of the two populations are unknown and it can be assumed the two populations have equal variances, we must use a t distribution with (let n₁ be the size of sample 1 and n₂ the size of sample 2)

Exhibit 10-11 An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below. We are interested in determining if the accident proportions differ between the two age groups. -Refer to Exhibit 10-11 and let p_u represent the proportion under and po the proportion over the age of 18. The null hypothesis is

Exhibit 10-2 The following information was obtained from matched samples. The daily production rates for a sample of workers before and after a training program are shown below. -Refer to Exhibit 10-2. The null hypothesis to be tested is H₀: $\mu$ _d = 0. The test statistic is

Exhibit 10-7 In order to estimate the difference between the average hourly wages of employees of two branches of a department store, the following data have been gathered. -Refer to Exhibit 10-7. A 95% interval estimate for the difference between the two population means is

A credit company has gathered information regarding the average amount owed by people under 30 years old and by people over 30 years. Independent random samples were taken from both age groups. You are given the following information. Construct a 95% confidence interval for the difference between the average amounts owed by the two age groups.

Maxforce, Inc., manufactures racquetball racquets by two different manufacturing processes (A and B). Because the management of this company is interested in estimating the difference between the average time it takes each process to produce a racquet, they select independent samples from each process. The results of the samples are shown below. a.Develop a 95% confidence interval estimate for the difference between the average time of the two processes. b.Is there conclusive evidence to prove that one process takes longer than the other? If yes, which process? Explain.

During the primary elections of 1996, candidate A showed the following pre-election voter support in Tennessee and Mississippi. a.Develop a 95% confidence interval estimate for the difference between the proportion of voters favoring candidate A in the two states. b.Is there conclusive evidence that one of the two states had a larger proportion of voters' support? If yes, which state? Explain.

The reliability of two types of machines used in the same manufacturing process is to be tested. The first machine failed to operate correctly in 90 out of 300 trials while the second type failed to operate correctly in 50 out of 250 trials. a.Give a point estimate for the difference between the population proportions of these machines. b.Calculate the pooled estimate of the population proportion. c.Carry out a hypothesis test to check whether there is a statistically significant difference in the reliability for the two types of machines using a .10 level of significance.

Exhibit 10-1 Salary information regarding male and female employees of a large company is shown below. -Refer to Exhibit 10-1. The standard error for the difference between the two means is

Independent random samples taken on two university campuses revealed the following information concerning the average amount of money spent on textbooks during the fall semester. We want to determine if, on the average, students at University A spent more on textbooks then the students at University B. a.Compute the test statistic. b.Compute the p-value. c.What is your conclusion? Let $\alpha$ = .05.

Exhibit 10-6 The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card. You are given the following information. -Refer to Exhibit 10-6. A point estimate for the difference between the mean purchases of the users of the two credit cards is

A comparative study of organic and conventionally grown produce was checked for the presence of E. coli. Results are summarized below. Is there a significant difference in the proportion of E. Coli in organic vs. conventionally grown produce? Test at $\alpha$ = 0.10.

From production line A, a sample of 500 items is selected at random, and it is determined that 30 items are defective. In a sample of 300 items from production process B (which produces identical items to line A), there are 12 defective items. Determine a 95% confidence interval estimate for the difference between the proportion of defectives in the two lines.

Two independent random samples of annual starting salaries for individuals with masters and bachelors degrees in business were taken and the results are shown below a.What are the degrees of freedom for the t distribution? b.Provide a 95% confidence interval estimate for the difference between the salaries of the two groups.

The office of records at a university has stated that the proportion of incoming female students who major in business has increased. A sample of female students taken several years ago is compared with a sample of female students this year. Results are summarized below. Has the proportion increased significantly? Test at $\alpha$ = 0.10.

Recently, a local newspaper reported that part time students are older than full time students. In order to test the validity of its statement, two independent samples of students were selected. a.Give the hypotheses for the above. b.Determine the degrees of freedom. c.Compute the test statistic. d.At 95% confidence, test to determine whether or not the average age of part time students is significantly more than full time students.

Exhibit 10-4 The following information was obtained from independent random samples. Assume normally distributed populations with equal variances. -Refer to Exhibit 10-4. The standard error of is

A poll was taken this year asking college students if they considered themselves overweight. A similar poll was taken five years ago. Results are summarized below. Has the proportion increased significantly? Let $\alpha$ = 0.05.