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

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. After Before Sample size 45 58 Mean in days) 4.6 4.9 Standard Deviation \sigma ) 0.5 0.6 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 α = 0.05.

When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as

In order to improve the grades of students at UTC, several incentive programs have been introduced. Results of random samples of grades from after and before the incentive programs are given below. After Incentives Before incentives Sample Size 14.00 12.00 Sample Mean 2.85 2.61 Sample Standard Deviation 0.40 0.35 Sample Mode 2.50 3.00 a. Give the hypotheses. b. Compute the test statistic. c. At a 0.1 level of significance, test to determine whether the incentive programs have significantly increased the average grades.

The level of significance

Exhibit 10-13 Part of an ANOVA table is shown below. Source of Sum of Degrees Mean Variation Squares of Freedom Square F Between Treatments 64 8 Within Treatments 2 Error Total 100 -Refer to Exhibit 10-13. The conclusion of the test is that the means

In order to determine whether or not the means of two populations are equal,

Which of the following is not a required assumption for the analysis of variance?

Exhibit 10-5 The following information was obtained from matched samples. Individual Method 1 Method 2 1 7 5 2 5 9 3 6 8 4 7 7 5 5 6 -Refer to Exhibit 10-5. The null hypothesis tested is H0: ?d = 0. The test statistic for the difference between the two population means is

In order to estimate the difference between the average age of male and female employees at the Young Corporation, the following information was gathered. Male Female Sample Size 32 36 Sample Mean 25 23 Sample Standard Deviation 4 6 Develop a 95% confidence interval estimate for the difference between the average age of male and female employees at the Young Corporation.

In an analysis of variance problem if SST = 120 and SSTR = 80, then SSE is

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

An experimental design where the experimental units are randomly assigned to the treatments is known as

The p-value

Three universities in your state decided to administer the same comprehensive examination to the recipients of MBA degrees from the three institutions. From each institution, MBA recipients were randomly selected and were given the test. The following table shows the scores of the students from each university. Northern Central Southern Univarsity University University 75 85 80 80 89 81 84 86 84 85 88 79 81 83 85 At α = 0.01, test to see if there is any significant difference in the average scores of the students from the three universities. Note that the sample sizes are not equal.) Use both the critical and p-value approaches.

An ANOVA procedure is used for data obtained from four populations. Four samples, each comprised of 30 observations, were taken from the four populations. The numerator and denominator respectively) degrees of freedom for the critical value of F are

When the p-value is used for hypothesis testing, the null hypothesis is not rejected if the

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. University A University B Sample Size 50 40 Average Purchase \ 260 \ 250 Standard Deviation \sigma) \ 20 \ 23 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 ? = .05.

Exhibit 10-14 The following is part of an ANOVA table that was obtained from data regarding three treatments and a total of 15 observations. Source of Variation Sum of Squares Degrees of Freedom Between Treatments 64 Error Within Treatments) 96 -Refer to Exhibit 10-14. The mean square between treatments MSTR) is

Exhibit 10-11 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. SSTR = 200 Sum Square Between Treatments) SST = 800 Total Sum Square) -Refer to Exhibit 10-11. The number of degrees of freedom corresponding to between treatments is

The following information regarding the number of semester hours taken from random samples of day and evening students is provided. Day Evening 16 12 s 4 2 n 140 160 Develop a 95% confidence interval estimate for the difference between the mean semester hours taken by the two groups of students.