12.3A manager is interested in testing whether three populations of interest have equal population means Simple random samples of size 10 were selected from each population. The following ANOVA table and related statistics were computed:

Applied Stats for Managers Homework Assignment Week 6

Linda H. Kalashian

Southern New Hampshire University, Manchester, NH

Section 12.1

Problem:

12.3A manager is interested in testing whether three populations of interest have equal population means Simple random samples of size 10 were selected from each population. The following ANOVA table and related statistics were computed:

	ANOVA: Single Factor
	Summary
Groups	Count	Sum	Average	Variance
Sample 1	10	507.18	50.72	35.06
Sample 2	10	405.79	40.58	30.08
Sample 3	10	487.64	48.76	23.13
	ANOVA
Source	SS	df	MS	F	p-value	F-crit
Between Groups	578.78	2	289.39	9.84	0.0006	3.354
Within Groups	794.36	27	29.42
Total	1,373.14	29

1. State the appropriate null and alternative hypotheses.The appropriate hypotheses are:

                                               
 Not all  are equal.

• Based on your answer to part a, what conclusions can be reached about the null and alternative hypothesis. Use a 0.05 level of significance. , therefore reject the Ho. P-value = 0.0006< =0.05, reject the Ho.

• If warranted, use the Turkey-Kramer procedure for multiple comparisons to determine which populations have different means. (Assume a=0.05.) range = 6.0;

12.5 Respond to each of the following questions using this partially completed one-way ANOVA table:

Source of Variation	SS	df	MS	F-ratio
Between Samples		3
Within Samples	405
Total	888	31

1. How many different populations are being considered in this analysis?
2. Fill on the ANOVA table with the missing values.
3. State the appropriate null and alternative hypotheses.Ho: . HA:

There are two different population means.

• Based on the analysis of variance F-test, what conclusion should be reached regarding the null hypothesis? Test using a=0.05.11.1309 > 2.9467, reject the Ho.

Section 12.2

Problem:

12.18A study was conducted to determine if differences in new textbook prices exist between on-campus bookstores, off campus bookstores, and Internet bookstores. To control for differences in textbook prices that might exist across disciplines, the study randomly selected 12 textbooks and recorded the price of each of the 12 books at each of the three retailers. You may assume normality and equal-variance assumptions have been met. The partially completed ANOVA table based on the study’s findings is show here:

ANOVA
Source of variation	SS	df	MS	F
Textbooks	16,624
Retailer	2.4
Error
Total	17477.6

1. Complete the ANOVA table by filling in the missing sums of squares. The degrees of freedom for each source, the mean square, and the calculated F-test statistic for each possible hypothesis test.

• Based on the study’s findings, was it correct to block for differences in textbooks? Conduct the appropriate test at the a=0.10 level of significance.F= 9.84 > critical F = 3.35, we reject the null hypothesis andconclude that the population means are not all equal.
• Based on the study’s findings, can it be concluded that there is a difference in the average price of the textbooks across three retail outlets? Conduct the appropriate hypothesis test at the a=0.10 level of significance.

 = not all are equal.

12.20The following ANOVA table and accompanying information are the result of a randomized block ANOVA test.

ANOVA
Source of Variation	SS	df	MS	F	p-value	F-crit
Rows	199,899	7	28557.0	112.8	0.0000	2.488
Columns	11,884	3	3961.3	15.7	0.0000	3.073
Error	5317	21	253.2
Total	217100	31

1. How many blocks were used in this study?r-1=7. R=7+1. r= 8
2. How many populations are involved in this test?
3. Test to determine whether blocking is effective using an alpha level equal to 0.05.Because the p-value < the alpha of 0.05 we do not reject the null hypothesis and conclude that blocking is effective.
4. Test the main hypothesis of interest using a=0.05.
5. If warranted, conduct an LSD test with a=0.05 to determine which population means are different.

Section 12.32

Problem:

12.32Examine the following two-factor analysis of variance table:

Source	SS	df	MS	F-Ratio
Factor A	162.79	4
Factor B			28.12
AB Interaction	262.31	12
Error
Total	1298.74	84

1. Complete the analysis of variance table.Fail to reject the Ho –Not enough sufficient evidence to conclude that at least two levels of Factor B have different means responses.
2. Determine if interaction exists between factor A and Factor B. Use a=0.05.Reject the Ho –Enough sufficient evidence to conclude that at least two levels of Factor B have different means responses.
3. Determine if the levels of factor A have equal means. Use a significance level of 0.05.Fail to reject the Ho. Not enough sufficient evidence to conclude that at least two levels of Factor B have different means responses.

12.33Consider the following data for a two-factor experiment:

	Factor A
Factor B	Level 1	Level 2	Level 3
	33	30	21
Level 1	31	42	30
	35	36	30
	23	30	21
Level 2	32	27	33
	27	25	18

1. Based on the sample data, do factors A and B have significant interaction? State the appropriate null and alternative hypotheses and test using a significance level of 0.05.0.4617 < 3.8853, do not reject the Ho.
2. Based on these sample data, can you conclude that the levels of factor A have equal means? Test using a significance level of 0.05.2.3766 < 3.8853, do not reject the Ho.
3. Do the data indicate that the levels of factor B have difference means? Test using a significance level equal to 0.05.5.7532 > 4.47472, reject the Ho.

 

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