Question

Let's now perform a mean-matched pairs test to test the claim that there is no mean difference between the age of males and females. For the context of this problem, d=x2−x1where the first data set represents actress (female) ages and the second data set represents male (actor) ages. We'll continue to use a significance of 0.05. You believe the population of difference scores is normally distributed, but you do not know the standard deviation.

H0: μd=0

H1:μd≠0

Actress Age	Actor Age
26	46
26	32
25	31
26	60
25	67
25	55
22	57
26	58
28	37
25	62
28	38
33	53
24	33
36	57
35	36

What is the critical value for this test? t=± (Round to three decimal places.)

What is the test statistic for this sample? t= (Round to three decimal places.)

What is the p-value? (Round to three decimal places.)

Conclusion about the null: A)Fail to support the null hypothesis.

B)Reject the null hypothesis.

C)Support the null hypothesis.

D)Fail to reject the null hypothesis.

Conclusion about the claim: A)Fail to reject the claim that there is no mean difference in the ages.

   B)There is insufficient evidence to support the claim that there is no mean difference in the ages.

   C)Support the claim that there is no mean difference in the ages.

D)Reject the claim that there is no mean difference in the ages.

Answer 1

Date: 01/05/2019 Answe To test the hypothesis is that there is a mean difference between the age of males and females at 5% significance level. The null and alternative hypothesis is, The t-test statistics is, By using Excel software, find t-test statistics with the help of following steps: 1) Import the data. menu 3) Select Variable 1 Range and Variable 2 Range. 4)Give Hypothesized Mean Difference 5) Select Labels and give Alpha 6) Choose Output Range from Output options 7) Click Ok.

t-Test: Paired Two Sample for Means Actor Age Actress Age Mean Variance Observations Pearson Correlation Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tal P(T<-t) two-tail t Critical two-tail 48.13333333 27.33333333 155.4095238 16.80952381 15 15 0.079192328 0 14 5.99920768 1.62961E-05 1.761310115 3.25921E-05 2.144786681 From the Excel output, the t-test statistics is 5.999 The t-critical value is, From the Excel output, the t-critical value is+ 2.145

The p-value for this test is, From the Excel output, thep-value for this test is 0.000 Decision The conclusion is that p-value in this context is less than 0.05 which is 0.000, so the null hypothesis is rejected at 5% level of significance. The answer is B Conclusion There is sufficient evidence to indicate that there is a mean difference between the age of males and females. The result is statistically significant. The answer is B