Exam 10: Comparisons Involving Means, Experimental Design and Analysis of Variance

Consider the following results for two samples randomly taken from two normal populations with equal variances. a.Develop a 95% confidence interval for the difference between the two population means. b.Is there conclusive evidence that one population has a larger mean? Explain.

Exhibit 10-5 The following information was obtained from matched samples. -Refer to Exhibit 10-5. The null hypothesis tested is H₀: $\mu$ _d = 0. The test statistic for the difference between the two population means is

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 95% confidence interval estimate for the difference between the average purchases of the customers using the two different credit cards is

The management of Regional Hospital has made substantial improvements in their hospital and would like to test and determine whether there has been a significant decrease in the average length of stay of their patients in their hospital. The following data has been accumulated from before and after the improvements. At 95% confidence, test to determine if there has been a significant reduction in the average length of stay. a.Formulate the hypotheses. b.Compute the test statistic. c.Using the p-value approach, test to see if the average length of stay in RFH is significantly less than the average length of stay in GH. Let $\alpha$ = 0.05.

If two independent large samples are taken from two populations, the sampling distribution of the difference between the two sample means

The critical F value with 6 numerator and 60 denominator degrees of freedom at $\alpha$ = .05 is

A company attempts to evaluate the potential for a new bonus plan by selecting a sample of 4 salespersons to use the bonus plan for a trial period. The weekly sales volume before and after implementing the bonus plan is shown below. (For the following matched samples, let the difference "d" be d = after - before.) a.State the hypotheses. b.Compute the test statistic. c.Use Alpha = .05 and test to see if the bonus plan will result in an increase in the mean weekly sales.

Independent simple random samples are taken to test the difference between the means of two populations whose variances are known. The sample sizes are n₁ = 38 and n₂ = 42. The correct distribution to use is the

When an analysis of variance is performed on samples drawn from K populations, the mean square between treatments (MSTR) is

Eight observations were selected from each of 3 populations (total of 24 observations), and an analysis of variance was performed on the data. The following are part of the results. Using $\alpha$ = .05, test to see if there is a significant difference among the means of the three populations.

The daily production rates for a sample of factory workers before and after a training program are shown below. Let d = After - Before. We want to determine if the training program was effective. a.Give the hypotheses for this problem. b.Compute the test statistic. c.At 95% confidence, test the hypotheses. That is, did the training program actually increase the production rates?

In order to determine whether or not a driver's education course improves the scores on a driving exam, a sample of 6 students were given the exam before and after taking the course. The results are shown below. Let d = Score After - Score Before. a.Compute the test statistic. b.At 95% confidence using the p-value approach, test to see if taking the course actually increased scores on the driving exam.

Exhibit 10-3 A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information. -Refer to Exhibit 10-3. The test statistic for the difference between the two population means is

The standard error of is the

Random samples of employees from three different departments of MNM Corporation showed the following yearly incomes (in $1,000). At $\alpha$ = .05, test to determine if there is a significant difference among the average incomes of the employees from the three departments. Use both the critical and p-value approaches.

Exhibit 10-12 In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations). The following information is provided. -Refer to Exhibit 10-12. The number of degrees of freedom corresponding to within treatments is

Exhibit 10-12 In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations). The following information is provided. -Refer to Exhibit 10-12. If at 95% confidence we want to determine whether or not the means of the five populations are equal, the p-value is

Exhibit 10-12 In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations). The following information is provided. -Refer to Exhibit 10-12. The number of degrees of freedom corresponding to between treatments is

Exhibit 10-1 Salary information regarding male and female employees of a large company is shown below. -Refer to Exhibit 10-1. At 95% confidence, the conclusion is the

Exhibit 10-11 To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments. You are given the results below. -Refer to Exhibit 10-11. The test statistic to test the null hypothesis equals