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researchers wanted to measure the effect of alcohol on the development of the hippocampal region in...

researchers wanted to measure the effect of alcohol on the development of the hippocampal region in adolescents. The researchers randomly selected 12 adolescents with alcohol use disorders. They wanted to determine whether hippcampal volumes in the alcoholic adolescents were less than the normal volume of 9.02 cubed. An analysis of the sample data revealed that the hippcampal volume is approximately normal with x =8.28 and s =0.8 conduct an appropriate test at the a =0.05 level of significance. Find the test statistic to=? The P=value is? Is there sufficient or not sufficient evidence that the hippcampal volumes are less or greater than the normal of 9.02 cubed?

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The provided sample mean is X = 8.28 and the sample standard deviation is s 0.8, and the sample size is n 12. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: μ 29.02 This corresponds to a left-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used. (2) Rejection Region Based on the information provided, the significance level is α 0.05, and the critical value for a left-tailed test is t,--1.796. The rejection region for this left-tailed test is R-t : t 〈-1.796(3) Test Statistics The t-statistic is computed as follows: fA -Ho 8.28 - 9.02 /Vn0.8/v12 8vn 0.8/3.204 (4) Decision about the null hypothesis Since it is observed that t- -3.204 < te-1.796, it is then concluded that the null hypothesis is rejected. Using the P-value approach: The p-value is p 0.0042, and since p 0.0042 < 0.05, it is concluded that the null hypothesis is rejected(5) Final conclusion

Therefore there is sufficient evidence that the hippcampal volumes are less than the normal of 9.02 cube.

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