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 the actual height was compared to the height given in that person's online profile. The differences between the onlineprofile height and the actual height (profile - actual) were used to compute the values in the accompanying table.Menx = 0.56$ = 0.81n = 40Womenx = 0.01$ = 0.75Find the df.df = 39n = 40You 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 believed that their samples were representative of these populations, participants were volunteers recruited throughnewspaper advertisements, so we should be a bit hesitant to generalize results to all online daters.)(a) Use the paired t test to determine if there is convincing evidence that, on average, male online daters overstate their height in online dating profiles. Use a = 0.05. (Used=profile - actual)Find the test statistic. (Round your answer to two decimal places.)t = 4.37✔Use technology to find the P-value. (Round your answer to four decimal places.)P-value=0.0000State your conclusion.O Reject H. We do not have convincing evidence that male online daters overstate their height in online dating profiles.O Fail to reject H. We do not have convincing evidence that male online daters understate their height in online dating profiles.ⒸReject H. We have convincing evidence that male online daters overstate their height in online dating profiles.O Fail to reject H. We have convincing evidence that male online daters overstate their height in online dating profiles.(b) Construct and interpret a 95% confidence interval for the difference between the mean online dating profile height and mean actual height for female online daters. (Use technology to calculate the critical value. Use profile actual Round your answers to three decimal places.)x) inches-0.150X0.330Interpret the interval.ⒸWe are 95% confident that the true mean online dating profile height is between these two values.O We are 95% confident that the true difference in mean online dating profile height and mean actual height for female online daters is between these two values.O There is a 95% chance that the true mean online dating profile height is directly in the middle of these two values.O We are 95% confident that the true mean actual height for female online daters is between these two values.O There is a 95% chance that the true differencemean online dating profile height and mean actual height for female online daters is directly in the middlethese two values.(c) Use the two-sample t test of Section 11.1 to test H: HH, = 0 versus H:-, 0, where is the mean height difference (profile - actual) for male online daters and w, is the 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 = 2.69xFind the df. (Round your answer down to the nearest whole number.)df = 77Use technology to find the P-value. (Round your answer to four decimal places.)P-value=0.0043xState 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.Ⓒ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 H. 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 from independent samples, while part (b) used a two-sample t test because the males and females were connected.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 number of males andfemales.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 number of males andfemales.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 from independent samples.

Question

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 the actual height was compared to the height given in that person's online profile. The differences between the onlineprofile height and the actual height (profile - actual) were used to compute the values in the accompanying table.Menx = 0.56$ = 0.81n = 40Womenx = 0.01$ = 0.75Find the df.df = 39n = 40You 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 believed that their samples were representative of these populations, participants were volunteers recruited throughnewspaper advertisements, so we should be a bit hesitant to generalize results to all online daters.)(a) Use the paired t test to determine if there is convincing evidence that, on average, male online daters overstate their height in online dating profiles. Use a = 0.05. (Used=profile - actual)Find the test statistic. (Round your answer to two decimal places.)t = 4.37✔Use technology to find the P-value. (Round your answer to four decimal places.)P-value=0.0000State your conclusion.O Reject H. We do not have convincing evidence that male online daters overstate their height in online dating profiles.O Fail to reject H. We do not have convincing evidence that male online daters understate their height in online dating profiles.ⒸReject H. We have convincing evidence that male online daters overstate their height in online dating profiles.O Fail to reject H. We have convincing evidence that male online daters overstate their height in online dating profiles.(b) Construct and interpret a 95% confidence interval for the difference between the mean online dating profile height and mean actual height for female online daters. (Use technology to calculate the critical value. Use profile actual Round your answers to three decimal places.)x) inches-0.150X0.330Interpret the interval.ⒸWe are 95% confident that the true mean online dating profile height is between these two values.O We are 95% confident that the true difference in mean online dating profile height and mean actual height for female online daters is between these two values.O There is a 95% chance that the true mean online dating profile height is directly in the middle of these two values.O We are 95% confident that the true mean actual height for female online daters is between these two values.O There is a 95% chance that the true differencemean online dating profile height and mean actual height for female online daters is directly in the middlethese two values.(c) Use the two-sample t test of Section 11.1 to test H: HH, = 0 versus H:-,> 0, where is the mean height difference (profile - actual) for male online daters and w, is the 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 = 2.69xFind the df. (Round your answer down to the nearest whole number.)df = 77Use technology to find the P-value. (Round your answer to four decimal places.)P-value=0.0043xState 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.Ⓒ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 H. 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 from independent samples, while part (b) used a two-sample t test because the males and females were connected.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 number of males andfemales.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 number of males andfemales.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 from independent samples.

Accepted Answer

Confidence interval is used to determine the range where the true value of the parameter lies. It…