9.2 A paper describes an investigation in which 40 men and 40 women with online dating profiles agreed to participate in a study. Each participant's height (in inches) was measured and theactual height was compared to the height given in that person's online profile. The differences between the online profile height and the actual height (profile - actual) were used tocompute the values in the accompanying table.MenWomenX = 0.56X = 0.07Sa = 0.81S = 0.75n = 40n = 40n USE SALTYou can assume it is reasonable to regard the two samples in this study as being representative of male online daters and female online daters. (Although the authors of the paper believedthat their samples were representative of these populations, participants were volunteers recruited through newspaper advertisements, so we should be a bit hesitant to generalize resultsto all online daters.) (c) Use the two-sample t test of Section 11.1 to test H,: Hm - H = 0 versus H: Hm - Hp 0, where um is the mean height difference (profile - actual) for male online daters and µe isthe mean height difference (profile - actual) for female online daters. (Use a = 0.05.)Find the test statistic. (Round your answer to two decimal places.)t =Find the df. (Round your answer down to the nearest whole number.)df =Use technology to find the P-value. (Round your answer to four decimal places.)P-value =State your conclusion.O Fail to reject H.. We do not have evidence that mean height difference for male online daters is greater than mean height difference for female online daters.O Reject H.. We do not have evidence that mean height difference for male online daters is greater than mean height difference for female online daters.O Reject H,. We have convincing evidence that mean height difference for male online daters is greater than mean height difference for female online daters.O Fail to reject Hp. We have convincing evidence that mean height difference for male online daters is greater than mean height difference for female online daters.(d) Explain why a paired t test was used in part (a) but a two-sample t test was used in part (c).O Part (a) used a paired t test because the profile and actual heights were connected, while part (b) used a two-sample t test because the males and females were fromindependent samples.O Part (a) used a paired t test because there were the same number of profile and actual heights, while part (b) used a two-sample t test because there were a different numberof males and females.O Part (a) used a paired t test because there were a different number of profile and actual heights, while part (b) used a two-sample t test because there were the same numberof males and females.O Part (a) used a paired t test because the profile and actual heights were from independent samples, while part (b) used a two-sample t test because the males and females wereconnected.

Question

9.2 A paper describes an investigation in which 40 men and 40 women with online dating profiles agreed to participate in a study. Each participant's height (in inches) was measured and theactual height was compared to the height given in that person's online profile. The differences between the online profile height and the actual height (profile - actual) were used tocompute the values in the accompanying table.MenWomenX = 0.56X = 0.07Sa = 0.81S = 0.75n = 40n = 40n USE SALTYou can assume it is reasonable to regard the two samples in this study as being representative of male online daters and female online daters. (Although the authors of the paper believedthat their samples were representative of these populations, participants were volunteers recruited through newspaper advertisements, so we should be a bit hesitant to generalize resultsto all online daters.) (c) Use the two-sample t test of Section 11.1 to test H,: Hm - H = 0 versus H: Hm - Hp > 0, where um is the mean height difference (profile - actual) for male online daters and µe isthe mean height difference (profile - actual) for female online daters. (Use a = 0.05.)Find the test statistic. (Round your answer to two decimal places.)t =Find the df. (Round your answer down to the nearest whole number.)df =Use technology to find the P-value. (Round your answer to four decimal places.)P-value =State your conclusion.O Fail to reject H.. We do not have evidence that mean height difference for male online daters is greater than mean height difference for female online daters.O Reject H.. We do not have evidence that mean height difference for male online daters is greater than mean height difference for female online daters.O Reject H,. We have convincing evidence that mean height difference for male online daters is greater than mean height difference for female online daters.O Fail to reject Hp. We have convincing evidence that mean height difference for male online daters is greater than mean height difference for female online daters.(d) Explain why a paired t test was used in part (a) but a two-sample t test was used in part (c).O Part (a) used a paired t test because the profile and actual heights were connected, while part (b) used a two-sample t test because the males and females were fromindependent samples.O Part (a) used a paired t test because there were the same number of profile and actual heights, while part (b) used a two-sample t test because there were a different numberof males and females.O Part (a) used a paired t test because there were a different number of profile and actual heights, while part (b) used a two-sample t test because there were the same numberof males and females.O Part (a) used a paired t test because the profile and actual heights were from independent samples, while part (b) used a two-sample t test because the males and females wereconnected.

Accepted Answer

The two- sample t test is useful to compare the means of two independent sample groups. The formula…