2. (20pts) Many students have been conducted to test the effects of marijuana us
ID: 2907742 • Letter: 2
Question
2. (20pts) Many students have been conducted to test the effects of marijuana use on mental abilities. In one such study, group of light and heavy users of marijuana in college were tested for memory recall, with the results given as follow: Light marijuana users n 64, 47 yers, s-7.2 years. Heavy marijuana users n 60, 43.9 years, s 5.9 years. Use a 0.05 significance level to test the claim that population of heavy marijuan users has a lower mean than the lights users. Should marijuana use be of concer to college students? a. claim/(Question: Popviaton of heavy m arijva n Usuers hare lower man than th lht users. Hypothesis: Test distribution:Explanation / Answer
Solution:-
2)
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: u1< u2
Alternative hypothesis: u1 > u2
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 1.1791
DF = 122
t = [ (x1 - x2) - d ] / SE
t = 2.63
tcritical = 1.657
Rejection region is t > 1.657.
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is thesize of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.
The observed difference in sample means produced a t statistic of 2.63.
Therefore, the P-value in this analysis is 0.005.
Interpret results. Since the P-value (0.005) is less than the significance level (0.05), we can reject the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that population of heavy marijauna users has a lower mean than the light users.
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