(c) Use the two-sample t test of Section 11.1 to test H: um - H = 0 versus H: Hm - µ> 0, where µ, is the mean height difference (profile - actual) for male online daters and u, 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 = 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 Ho. 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 Ho. 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 Ho. 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 from independent 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-samplet test because there were a different number of 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 number of 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 were connected.