A psychologist wants to test whether there is any difference in puzzle-solving abilities between boys and girls. Independent samples of nine boys and eight girls were chosen at random. The boys took a mean of 39 minutes to solve a certain puzzle, with a standard deviation of 4.1 minutes. The girls took a mean of 41 minutes to solve the same puzzle, with a standard deviation of 5.9 minutes. Assume that the two populations of completion times are normally distributed, and that the population variances are equal. Can we conclude, at the 0.05 level of significance, that the mean puzzle-solving times for boys, ?1 is less than the mean puzzle-solving times for girls, ?2?

(a) State the null hypothesis Ho and the alternative hypothesis H. H p Ho : I X S p H : I (b) Determine the type of test statistic to use. (Choose one) O=0 OSO 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) 0#0 00 X ? (d) Find the critical value at the 0.05 level of significance. (Round to three or more decimal places.) (e) Can we conclude that the mean puzzle-solving times for boys is less than the mean puzzle- solving times for girls? Yes No