Question

Many studies have been conducted to test the effects of marijuana use on mental abilities. In one such study, groups of light and heavy users of marijuana in college were tested for memory recall, with the results given below: Items sorted correctly by light marijuana users: n = 64, x-bar = 53.3, s = 3.6 Items sorted correctly by heavy marijuana users: n = 65, x-bar = 51.3, s = 4.5 Use a 0.01 significance level to test the claim that the population of heavy marijuana users has a lower mean than the population of light users.

Answer 1

Null hypothesis: H:44 Suz The population of heavy marijuana users has same mean as the population of light users. Alternative hypothesis: на: >, The population of heavy marijuana users has a lower mean than the population of light users. Rejection rule: If Z>2.326, then reject the null hypothesis H.

(X-X)-(1-4) Z= + n n2 (53.3-51.3)-0 13.6² 4.52 + V 64 65 2 0.7170 = 2.790 Test Value: 2.790. Conclusion: Use a significance level, a =0.01. Here the value of the test statistic 2.790, which is greater than the critical value 2.326. That is, 2(= 2.790) > 2.326. Therefore, by the rejection rule, reject the null hypothesis H. Interpretation: There is sufficient evidence at level of significance a = 0.01. The population of heavy marijuana users has a lower mean than the population of light users.