AP Statistics / Mr. Hansen
4/16/2002

Name: ________________________

1.

A poll of 3700 high school students (2200 seniors and 1500 juniors) finds that 60% of seniors, but only 58% of juniors, favor lowering the drinking age from 21 to 18.

 (a)

Is this difference significant? Show your work and conclusion.

(b)

Compute a 98% confidence interval for that difference. Show your work and state your interval in the context of the problem.

2.

Mr. Carroll raises plants from seedlings. Here are two sets of data for plant height, taken a week apart. The plants are all of the same species and are raised similarly.

Plant #

Week 1 height (inches)

Week 2 height (inches)

1
2
3
4
5
6
7
8
9

14.2
16.1
13.8
13.7
15.1
16.0
15.5
14.5
14.7

19.1
20.8
21.1
18.8
19.4
20.2
19.9
20.5
18.8

(a)

Compute a 95% confidence interval that is relevant to this problem and stated in context. Show your work.

(b)

Does Mr. Carroll have good evidence that plants of this type grow more than 4 inches, on average, between week 1 and week 2? Show all work.

(c)

Does Mr. Carroll have good evidence that plants of this type grow more than 5 inches, on average, between week 1 and week 2? This time, omit work but provide a brief explanation for your conclusion.

3.

Assuming that everything else remains unchanged, state briefly what happens to the standard error and p-value when we

(a)

change from a 1-sided to a 2-sided approach

(b)

increase the sample size (or if 2 samples, we increase both sample sizes) by a factor of 9

(c)

increase the s.d. of the sampling distribution (or if 2 samples, we increase the s.d. of both sampling distributions) by a factor of 9

4.

Repeat problem 2(b), but this time treat the two columns of height data as coming from independent populations of plants of different ages that were raised under similar growing conditions and measured all on the same day.