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Test of Hypothesis

The file attached will you give a strong understanding in testing the hypothesis. Particularly the questions are based on comparing the mean, comparing proportion and regression.

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#4 pg 502
Hypothesis Test for Effects of Marijuana Use on College Student: In a study of the effects of marijuana use , light and heavy users of marijuana in college were tested for memory recall with the results given below. Use a 0.05 significance level to test the claim that the population of heavy marijuana users has a standard deviation from that of light users.

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

Solution:

Null Hypothesis:
The population of heavy marijuana users has no standard deviation from that of light users.

Alternative Hypothesis:
The population of heavy marijuana users has a standard deviation from that of light users.

Critical Value:
Since the sample size greater we can use the Z-test statistics. The critical value from the Z-table at the 0.025 level of significance is 1.96 (since the test is two sided).

Test Statistics:
Z-test statistics is given by,

Z =

By plugging the values in the formula we have,

Z =

Z = = 2.7895

Decision Rule:
If the calculated value of Z is less than the table value then we can accept the null hypothesis. Otherwise reject the null and accept the alternative hypothesis.

Conclusion:
Since the calculated value of Z 2.7895 is greater than the critical value 1.96 we have to reject the null hypothesis and accept the alternative hypothesis that the population of heavy marijuana has a standard deviation from ...

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