A psychologist wants to test whether there is any difference in puzzle-solving abilities between boys and girls. Independent samples of eight boys and twelve girls were chosen at random. The boys took a mean of 32 minutes to solve a certain puzzle, with a standard deviation of 4.1 minutes. The girls took a mean of 34 minutes to solve the same puzzle, with a standard deviation of 3.8 minutes. Assume that the two populations of completion times are normally distributed. Can we conclude, at the 0.1 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 and the alternative hypothesis.

b. Find the value of the test statistic.

c. Find the critical value at the 0.01 level of significance.

d. Can we conclude that the mean puzzle-solving times for boys is less than the mean puzzle[1]solving times for girls?

e. Construct 95% confidence interval for the difference for mean puzzle-solving times for boys

and girls, 1 2, and interpret it.