Question

A car dealer is interested in comparing the average gas mileages of four different car models. The dealer believes that the average gas mileage of a particular car will vary depending on the person who is driving the car due to different driving styles. Because of this, he decides to use a randomized block design. He randomly selects five drivers and asks them to drive each of the cars. He then determines the average gas mileage for each car and each driver. Can the dealer conclude that there is a significant difference in average gas mileages of the four car models? The results of the study are as follows.

Question 1

Find the value of the F-test statistic for testing whether the average gas mileage is the same for the four car models. Round your answer to two decimal places, if necessary.

	Car A	Car B	Car C	Car D
Driver 1	23	39	22	25
Driver 2	37	39	28	39
Driver 3	39	40	21	25
Driver 4	34	36	27	33
Driver 5	27	35	26	37

a. Answer:

Question 2:

Make the decision to reject or fail to reject the null hypothesis that there is no difference in the average gas mileages of the four car models. State the conclusion in terms of the original problem. Use alpha = 0.01.

a. We reject the null hypothesis. At the 0.01 level of significance, there is sufficient evidence of a difference in average gas mileages of the four car models.

b. We fail to reject the null hypothesis. At the 0.01 level of significance, there is not sufficient evidence of a difference in average gas mileages of the four car models.

c. We fail to reject the null hypothesis. At the 0.01 level of significance, there is sufficient evidence of a difference in average gas mileages of the four car models.

d. We reject the null hypothesis. At the 0.01 level of significance, there is not sufficient evidence of a difference in average gas mileages of the four car models.

Question 3:

Was the dealer able to significantly reduce variation among the observed gas mileages by blocking? Use alpha 0.01.

a. The variation in gas mileages is significantly reduced by blocking since we reject the null hypothesis that the block means are the same at the 0.01 level of significance.

b. The variation in gas mileages is not significantly reduced by blocking since we reject the null hypothesis that the block means are the same at the 0.01 level of significance.

c. The variation in gas mileages is not significantly reduced by blocking since we fail to reject the null hypothesis that the block means are the same at the 0.01 level of significance.

d. The variation in gas mileages is significantly reduced by blocking since we fail to reject the null hypothesis that the block means are the same at the 0.01 level of significance.

Question 4:

A banana grower has three fertilizers from which to choose. He would like to determine which fertilizer produces banana trees with the largest yield (measured in pounds of bananas produced). The banana grower has noticed that there is a difference in the average yields of the banana trees depending on which side of the farm they are planted (South Side, North Side, West Side, or East Side), therefore, a randomized block design is used in the study. Because of the variation in yields among the areas on the farm, the farmer has decided to randomly select three trees within each area and then randomly assign the fertilizers to the trees. After harvesting the bananas, he calculates the yields of the trees within each of the areas. Can the banana grower conclude that there is a significant difference among the average yields of the banana trees for the three fertilizers? The results are as follows.

Find the value of the F-test statistic for testing whether the average yield is the same for the three fertilizers. Round your answer to two decimal places, if necessary.

Side of Farm	Fertilizer A	Fertilizer B	Fertilizer C
South Side	58	47	52
North Side	41	47	60
West Side	57	59	44
East Side	56	50	41

Answer:

Question 5:

Make the decision to reject or fail to reject the null hypothesis that there is no difference among the average yields of the banana trees for the three fertilizers. State the conclusion in terms of the original problem.

a. No answer text provided.

b. We reject the null hypothesis. At the 0.10 level of significance, there is not sufficient evidence of a difference among the average yields of the banana trees for the three fertilizers.

c. We fail to reject the null hypothesis. At the 0.10 level of significance, there is not sufficient evidence of a difference among the average yields of the banana trees for the three fertilizers.

d. No answer text provided.

Answer 1

Result:

Excel Addon Megastat used.

Randomized blocks ANOVA
	Mean	n	Std. Dev
	32.000	5	6.782	Car A
	37.800	5	2.168	Car B
	24.800	5	3.114	Car C
	31.800	5	6.573	Car D
	27.250	4	7.932	Driver 1
	35.750	4	5.252	Driver 2
	31.250	4	9.674	Driver 3
	32.500	4	3.873	Driver 4
	31.250	4	5.560	Driver 5
	31.600	20	6.644	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatments	424.40	3	141.467	6.39	.0078
Blocks	148.80	4	37.200	1.68	.2187
Error	265.60	12	22.133
Total	838.80	19

Question 1

Find the value of the F-test statistic for testing whether the average gas mileage is the same for the four car models. Round your answer to two decimal places, if necessary.

a. Answer: F= 6.39

Question 2:

Make the decision to reject or fail to reject the null hypothesis that there is no difference in the average gas mileages of the four car models. State the conclusion in terms of the original problem. Use alpha = 0.01.

a. We reject the null hypothesis. At the 0.01 level of significance, there is sufficient evidence of a difference in average gas mileages of the four car models.

Question 3:

Was the dealer able to significantly reduce variation among the observed gas mileages by blocking? Use alpha 0.01.

c. The variation in gas mileages is not significantly reduced by blocking since we fail to reject the null hypothesis that the block means are the same at the 0.01 level of significance.

Question 4:

A banana grower has three fertilizers from which to choose. He would like to determine which fertilizer produces banana trees with the largest yield (measured in pounds of bananas produced). The banana grower has noticed that there is a difference in the average yields of the banana trees depending on which side of the farm they are planted (South Side, North Side, West Side, or East Side), therefore, a randomized block design is used in the study. Because of the variation in yields among the areas on the farm, the farmer has decided to randomly select three trees within each area and then randomly assign the fertilizers to the trees. After harvesting the bananas, he calculates the yields of the trees within each of the areas. Can the banana grower conclude that there is a significant difference among the average yields of the banana trees for the three fertilizers? The results are as follows.

Randomized blocks ANOVA
	Mean	n	Std. Dev
	53.000	4	8.042	Fertilizer A
	50.750	4	5.679	Fertilizer B
	49.250	4	8.539	Fertilizer C
	52.333	3	5.508	South Side
	49.333	3	9.713	North Side
	53.333	3	8.145	West Side
	49.000	3	7.550	East Side
	51.000	12	6.994	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatments	28.50	2	14.250	0.18	.8373
Blocks	42.00	3	14.000	0.18	.9064
Error	467.50	6	77.917
Total	538.00	11

Find the value of the F-test statistic for testing whether the average yield is the same for the three fertilizers. Round your answer to two decimal places, if necessary.

Answer:F=0.18

Question 5:

Make the decision to reject or fail to reject the null hypothesis that there is no difference among the average yields of the banana trees for the three fertilizers. State the conclusion in terms of the original problem.

c. We fail to reject the null hypothesis. At the 0.10 level of significance, there is not sufficient evidence of a difference among the average yields of the banana trees for the three fertilizers.