Exam 13: Experimental Design and Analysis of Variance

Exhibit 13-7 The following is part of an ANOVA table, which was the results of three treatments and a total of 15 observations. -An ANOVA procedure is used for data obtained from five populations. five samples, each comprised of 20 observations, were taken from the five populations. The numerator and denominator (respectively) degrees of freedom for the critical value of F are

Exhibit 13-5 Part of an ANOVA table is shown below. -Refer to Exhibit 13-5. The mean square between treatments (MSTR) is

Exhibit 13-2 -Refer to Exhibit 13-2. The test statistic to test the null hypothesis equals

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

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

An ANOVA procedure is used for data that was obtained from four sample groups each comprised of five observations. The degrees of freedom for the critical value of F are

Exhibit 13-7 The following is part of an ANOVA table, which was the results of three treatments and a total of 15 observations. -Random samples were selected from three populations. The data obtained are shown below. At a 5% level of significance, test to see if there is a significant difference in the means of the three populations. (Please note that the sample sizes are not equal.)

Exhibit 13-7 The following is part of an ANOVA table, which was the results of three treatments and a total of 15 observations. -The manager of Young Corporation wants to determine whether or not the type of work schedule for her employees has any effect on their productivity. She has selected 15 production employees at random and then randomly assigned 5 employees to each of the 3 proposed work schedules. The following table shows the units of production (per week) under each of the work schedules. At a 5% level of significance determine if there is a significant difference in the mean weekly units of production for the three types of work schedules.

Random samples of individuals from three different cities were asked how much time they spend per day watching television. The results (in minutes) for the three groups are shown below. At $\alpha$ = 0.05, use Excel to test to see if there is a significant difference in the averages of the three groups.

To test whether the time required to fully load a standard delivery truck is the same for three work shifts (day, evening, and night), NatEx obtained the following data on the time (in minutes) needed to pack a truck. Use these data to test whether the population mean times for loading a truck differ for the three work shifts. Use $\alpha$ = .05.

In a completely randomized design involving three treatments, the following information is provided: The overall mean for all the treatments is

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

The final examination grades of random samples of students from three different classes are shown below. At the $\mu$ = .05 level of significance, is there any difference in the mean grades of the three classes?

Exhibit 13-6 Part of an ANOVA table is shown below. -Refer to Exhibit 13-6. The mean square between treatments (MSTR) is

Exhibit 13-7 The following is part of an ANOVA table, which was the results of three treatments and a total of 15 observations. -In a completely randomized experimental design, 7 experimental units were used for the first treatment, 9 experimental units for the second treatment, and 14 experimental units for the third treatment. Part of the ANOVA table for this experiment is shown below. a.Fill in all the blanks in the above ANOVA table. b.At a 5% level of significance, test to see if there is a significant difference among the means.

Exhibit 13-4 In a completely randomized experimental design involving five treatments, thirteen observations were recorded for each of the five treatments. The following information is provided.SSTR = 200 (Sum Square Between Treatments) SST = 800 (Total Sum Square) -Refer to Exhibit 13-4. The mean square within treatments (MSE) is

Ten observations were selected from each of 3 populations, and an analysis of variance was performed on the data. The following are the results: a.Using $\mu$ = .05, test to see if there is a significant difference among the means of the three populations. b.If in Part a you concluded that at least one mean is different from the others, determine which mean is different. The three sample means are = 24.8,= 23.4, and= 27.4. Use Fisher's LSD procedure and let $\mu$ = .05.

The three major automobile manufacturers have entered their cars in the Indianapolis 500 race. The speeds of the tested cars are given below. At $\mu$ = .05, test to see if there is a significant difference in the average speeds of the cars of the auto manufacturers.

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

Exhibit 13-4 In a completely randomized experimental design involving five treatments, thirteen observations were recorded for each of the five treatments. The following information is provided.SSTR = 200 (Sum Square Between Treatments) SST = 800 (Total Sum Square) -Refer to Exhibit 13-4. The sum of squares within treatments (SSE) is