2. Is crack whack? What are the effects of cocaine in utero on children? Childre
ID: 2946295 • Letter: 2
Question
2. Is crack whack? What are the effects of cocaine in utero on children? Children were tested at age 4 for object assembly skill (which requires visual and spatial skills related to mathematics). The 190 children born to cocaine users had a mean score of 7.3 and a standard deviation of 3.0. The 185 children not exposed had a mean score of 8.2 with a standard deviation of 3.0. Use at 0.05 significance level to test the claim that prenatal cocaine exposure is ssociated with lower scores of four year old children on the test of object assembly.Explanation / Answer
Solution:-
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 = 0.25216
DF = 373
t = [ (x1 - x2) - d ] / SE
t = - 3.57
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 - 3.57.
Therefore, the P-value in this analysis is less than 0.001
Interpret results. Since the P-value (less than 0.001) 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 prenatal cocaine exposure is associated with lower scores of four year old children on the test of object assembly.
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