Since we do not know σ , but do have a large sample size, we will use a t procedure.
, df = 100 – 1. Using df = 80 from Table B (rounding down from 99), we have0.05 < P -value < 0.10. Using a TI-83/84 with df = 99, the P -value =
tcdf(-100,-1.45,99)=0.075.
The 99% confidence interval will be more likely to contain the population value being estimated, but
will be wider than a 95% confidence interval.
- I. (a) We are 95% confident that the true difference between the mean age of male statistics
teachers and female statistics teachers is between –4.5 years and 3.2 years.
(b) Since 0 is contained in this interval, we do not have evidence of a statistically significant
difference between the mean ages of male and female statistics teachers.
II. (a) We are 95% confident that the true difference between the mean age of male statistics
teachers and female statistics teachers is between 2.1 years and 3.9 years.
(b) Since 0 is not in this interval, we do have evidence of a real difference between the mean
ages of male and female statistics teachers. In fact, since the interval contains only positive
values, we have evidence that the mean age of male statistics teachers is greater than the
mean age of female statistics teachers.
III. (a) We are 95% confident that the true difference between the mean age of male statistics
teachers and female statistics teachers is between –5.2 years and –1.7 years.
(b) Since 0 is not in this interval, we have evidence of a real difference between the mean
ages of male and female statistics teachers. In fact, since the interval contains only negative
values, we have evidence that the mean age of male statistics teachers is less than the mean
age of female statistics teachers. - t procedures are appropriate because the population is approximately normal. n = 20 df = 20 – 1
= 19 t * = 2.861 for C = 0.99. - (a) A Type I error is made when we mistakenly reject a true null hypothesis. In this situation, that
means that we would mistakenly reject the true hypothesis that the available housing is sufficient.
The risk would be that a lot of money would be spent on building additional housing when it
wasn’t necessary.
(b) A Type II error is made when we mistakenly fail to reject a false hypothesis. In this situation that
means we would fail to reject the false hypothesis that the available housing is sufficient. The
risk is that the university would have insufficient housing for its students.