Question

A new fever-reducing drug is being tested on 30 people. The ‘Problem 8’ show the time to relief (in minutes) for three ethnic groups divided by sex. Use 2-way ANOVA to see if there is (a) a difference between the means in the three groups; (b) a difference between male and female means; and (c) if there is any interaction between sex and ethnic group in the average time to relief for each group.

(a) test statistic:

(a) p-value:

(a) is there a difference between groups:

(b) test statistic:

(b) p-value:

(b) is there a difference between the sexes:

(c) Test statistic:

(c) P-value

(c) decision

(c) is there an interaction:

	White	Black	Latino
Male	34	53	53
	49	52	40
	49	43	36
	34	56	33
	26	42	39
Female	38	36	38
	39	41	31
	37	43	44
	46	37	30
	38	41	34

Answer 1

Date: 03/05/2019 Answer a) To test the hypothesis is that there is a difference between the means in the three groups at 5% level of significance. The null and alternative hypothesis is, Ha : at least one A, is unequal. The F-test statistics for groups is, By using Excel software, find F-test statistics with the help of following steps 1) Import the data. 2) Choose ANOVA: Two Factor With Replication from Data Analysis in Data menu 3) Choose Input Range. 4) Choose Output Range. 5) Click Ok.

ANOVA Source of Variation Sexes Groups Interaction Within P-value F crit MS 145.2 247.2 146.4 1030.4 1569.2 145.2 3.381988 0.078318 4.259677 123.6 2.878882 0.075741 3.402826 73.2 1.704969 0.203067 3.402826 2 2 24 42.93333 29 From the Excel output, the F-test statistics for groups is 2.88 The p-value for this test is, From the Excel output, thep value for this test is |0.0757 Decision The conclusion is that p-value in this context is higher than 0.05 which is 0.0757, so the null hypothesis is not rejected at 5% level of significance. There is insufficient evidence to indicate that there is a difference between the means in the three groups. The result is not statistically significant

b) To test the hypothesis is that there is a difference between male and female means at 5% level of significance. The null and alternative hypothesis is H, : at least one is unequal The F-test statistics for sexes is, From the Excel output in part (a), the F-test statistics for sexes is 3.38 . The p-value for this test is, From the Excel output in part (a), the p value for this test is0.0783 Decision

The conclusion is that p-value in this context is higher than 0.05 which is 0.0783, so the null hypothesis is not rejected at 5% level of significance. There is insufficient evidence to indicate that there is a difference between male and female means. The result is not statistically significant c) To test the hypothesis is that there is an interaction effect between sex and ethnic group in the average time to relief for each group at 5% level of significance. Thenull and alternative hypothesis is, The null hypothesis is that there is no interaction effect between sex and ethnic group in the average time to relief for each group. The alternative hypothesis is that there is an interaction effect between sex and ethnic group in the average time to relief for each group. The F-test statistics for interaction is, From the Excel output in part (a), the F-test statistics for interaction is 1.70

The p-value for this test is, From the Excel output in part (a), the p value for this test is 0.2031 Decision The conclusion is that p-value in this context is higher than 0.05 which is 0.2031, so the null hypothesis is not rejected at 5% level of significance. There is insufficient evidence to indicate that there is an interaction effect between sex and ethnic group in the average time to relief for each group. The result is not statistically significant