A psychologist wants to test whether there is any difference in puzzle-solving abilities between boys and girls. Independent samples of eight boys and eleven girls were chosen at random. The boys took a mean of 38 minutes to solve a certain puzzle, with a standard deviation of 4.5 minutes. The girls took a mean of 39 minutes to solve the same puzzle, with a standard deviation of 5.7 minutes. Assume that the two populations of completion times are normally distributed, and that the population variances are equal. Can we conclude, at the 0.01 level of significance, that the mean puzzle-solving times for boys, u, is less than the mean puzzle-solving times for girls, u,? Perform a one-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) The null hypothesis: H, :0 The alternative hypothesis: H :0 = The type of test statistic: (Choose one) v The value of the test statistic: (Round to at least three decimal places.) The critical value at the 0.01 level of significance: (Round to at least three decimal places.) Activate