The following data set shows the ages of the Best Actress and Best Actor award at a given awards show for various years: Actress Age Actor Age 33 64 31 64 36 54 23 35 34 36 29 67 27 49 25 60 36 45 31 49 29 56 22 67 30 51 37 31 37 38 Using a Sign Test, test the claim that there is no median difference between the ages of Best Actress and Best Actor award winners. Find the null and alternative hypothesis. H0:H0: Select an answer The median age of actresses is more than the median age of actors. The median of the differences is NOT zero. The median of the differences is zero. The median age of actresses is less than the median age of actors. H1:H1: Select an answer The median of the differences is zero. The median age of actresses is more than the median age of actors. The median of the differences is NOT zero. The median age of actresses is less than the median age of actors. If we consider + to represent when the female was older than the male, then how many of each sign is there? Positive Signs: Negative Signs: Total Signs: What is the p-value? (Round to three decimal places.) At a 0.025 significance, what is the conclusion about the null? Select an answer Reject the null hypothesis. Fail to reject the null hypothesis. Fail to support the null hypothesis. Support the null hypothesis. What is the conclusion about the claim? Select an answer Support the claim that there is no difference in median age. There is insufficient evidence to support the claim that there is no difference in median age. Fail to reject the claim that there is no difference in median age Reject the claim that there is no difference in median age. 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−x1d=x2-x1 where 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 0.025. You believe the population of difference scores is normally distributed, but you do not know the standard deviation. H0: μd=0H0: μd=0 H1:μd≠0H1:μd≠0 Actress Age Actor Age 33 64 31 64 36 54 23 35 34 36 29 67 27 49 25 60 36 45 31 49 29 56 22 67 30 51 37 31 37 38 What is the critical value for this test? t=±t=± (Round to three decimal places.) What is the test statistic for this sample? t=t= (Round to three decimal places.) What is the p-value? (Round to three decimal places.) Conclusion about the null: Select an answer Reject the null hypothesis. Fail to support the null hypothesis. Support the null hypothesis. Fail to reject the null hypothesis. Conclusion about the claim: Select an answer Support the claim that there is no mean difference in the ages. There is insufficient evidence to support the claim that there is no mean difference in the ages. Fail to reject the claim that there is no mean difference in the ages. Reject the claim that there is no mean difference in the ages. How were these two tests similar? How were these two tests different?