Please explain step by step!

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 girlstook 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, atthe 0.1 level of significance, that the mean puzzle-solving times for boys, 1 is less than the meanpuzzle-solving times for girls, 2?

a. State the null hypothesis and the alternative hypothesis.

b. Find the value of the test statistic. (Round to three or more decimal places.)

c. Find the critical value at the 0.01 level of significance. (Use table.)

d. Can we conclude that the mean puzzle-solving times for boys are less than the mean puzzle-solving times for girls?

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

and girls, 1 2, and interpret it.