In: Statistics and Probability
On average, do males start smoking at an earlier grade than females? Data from 94 12th grade boys that smoke and 108 12th grade females that smoke found that the mean grade of first use of cigarettes was 9.87 for boys (standard deviation of 1.75), and 10.17 for girls (standard deviation of 1.69).
a) Is this sufficient evidence at alpha =.05 that the mean grade
for first-time cigarette use is lower for boys than for girls? (10
points)
b) Calculate and interpret a 99.9% confidence interval for the mean
difference between all boys and girls in the mean grade of first
cigarette use. (6 points)
c) What is the margin of error for the confidence interval you calculate in part B? (2 points)
d) Based on the confidence interval you calculated in part B, we
are 99.9% confident (1 point)
i. That the mean grade for first-time cigarette use is lower for
boys than for girls.
ii. That the mean grade for first-time cigarette use is higher for
boys than for girls.
iii. That it is plausible that there is no difference in the mean
grade for first-time cigarette use between boys and girls.
iv. We can’t conclude anything at alpha=.001 based on this
confidence interval.
e) Calculate and interpret a 95% confidence interval for the mean
grade of first use of cigarettes for boys. (6 points)
There is insufficient evidence to conclude that the mean grade for first-time cigarette use is lower for boys than for girls.
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