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A psychologist wants to test whether there is any difference in puzzle-solving abilities between boys and girls. Independent samples of twelve boys and nine girls were chosen at random. The boys took a mean of 32 minutes to solve a certain puzzle, with a standard deviation of 4.4 minutes. The girls took a mean of 33 minutes to solve the same puzzle, with a standard deviation of 5.2 minutes. Assume that the two populations of completion times are normally distributed, and that the population variances are equal. Can we conclude, at the 0.10 level of significance, that the mean puzzle-solving times for boys, W is less than the mean puzzle-solving times for girls, U2? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) (a) State the null hypothesis /7, and the alternative hypothesis -1. O P Ho : M1 = uz X S p (b) Determine the type of test statistic to use. t Degrees of freedom: ] 0-0 030 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) 0*0 00 0 X 5 ? (d) Find the critical value at the 0.10 level of significance. (Round to three or more decimal places.) 0 (e) Can we conclude that the mean puzzle-solving times for boys is less than the mean puzzle- solving times for girls? OYes ONo

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