A study was conducted on pregnant women and the subsequent development of their children. One of...

A study was conducted on pregnant women and the subsequent development of their children. One of the questions of interest was whether the IQ of children would differ for mothers who smoked at least 10 cigarettes a day during pregnancy and those who did not smoke at all. The mean IQ at age 4 for the children of the 66 nonsmokers was 113.04 points, while for the children of the 47 smokers, it was 103.17 points. The standard deviations were not reported, but from other information that was provided, the pooled standard deviation was about 13.5 points.

(a) Assuming that these women and children are a representative sample, find a 95% confidence interval (use t *) for the difference in mean IQ scores at age 4 for children of mothers who do not smoke during pregnancy and those whose mothers smoke at least 10 cigarettes a day during pregnancy. Write a sentence interpreting the interval. (Round your answer to two decimal places.) ( , )

(b) One of the statements in the article was "after control for confounding background variables . . . the average difference observed at 36 and 48 months was reduced to 4.35 points (95% CI: 0.02, 8.68)." Explain the purpose of this statement, and interpret the result given. After adjustments for possible confounding variables, we can say with 95% confidence that the difference in mean IQ scores at age 4 is between ( ) and ( ) for children of mothers who.....

Expert Solution

a. 95% confidence interval for the difference in mean IQ scores at age 4 for children of mothers who do not smoke during pregnancy and those whose mothers smoke at least 10 cigarettes a day during pregnancy:

(4.7642,14.9758) is range of values that we can be 95% certain contains the difference of population means of IQ scores at age 4 for children of mothers who do not smoke during pregnancy and those whose mothers smoke at least 10 cigarettes a day during pregnancy and since the CI contains all positive values hence we conclude that IQ scores at age 4 for children of mothers who do not smoke during pregnancy is significantly higher than those whose mothers smoke at least 10 cigarettes a day during pregnancy at 5% level of significance.

b.

95% confidence that the difference in mean IQ scores at age 4 is

After control for confounding background variables, lower boundary of the CI is very closed to zero hence we conclude that IQ of the children for mothers who smoked after control is improved.

orchestra answered 1 year ago

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