Math 37 - HW 7

Math 37 - HW 7

Practice Assignment (to be discussed randomly Wednesday, March 10)

1) (p. 447) 6.2

2) A survey conducted by Newsweek on June 2-3, 1994, asked adult Americans, "Do you think the United States is in a moral and spiritual decline?" Of the 748 adults surveyed, 76% answered "yes". For the survey discussed, identify the following 4 statements as true or false:

The survey's margin of error guarantees that the population proportion p is within .03 of .76.
The probability is .95 that p falls within the confidence interval
If one repeatedly took samples of 748 adult Americans, asked them the survey question, and formed confidence intervals in this same manner, then in the long run 95% of the intervals so generated would contain the true value of the population proportion p.
If one repeatedly took random samples of 748 adult Americans, asked them the survey question, and formed confidence intervals in this same manner, then in the long run 95% of the intervals so generated would contain the value of .76.

3) How common is behavior that puts people at risk of AIDS? The National AIDS Behavior Surveys interviewed a random sample of 2673 adult heterosexuals. Of these, 170 said they had multiple sexual partners in the past year.

(a) Explain in plain language what the parameter p is in this setting.

(b) Give a 95% confidence interval for the proportion of all adult heterosexuals who have multiple partners. Then explain carefully, to someone who knows no statistics, what the confidence interval tells us about sexual behavior.

(c) What type of nonsampling error is likely to affect the results of this survey? Does the confidence interval in (a) take nonsampling errors into account?

Homework Assignment (due Friday, March 12)

1) (p. 448) 6.5, 6.11, 6.14 and (c) Based on the results in (a), do you think the scale is balanced?

2) (p. 452) 6.20

3) 8.2 (p. 596)

4) Below are the heights reported for students in Math 37 this semester.

65.0 65.0 65.0 65.0 66.0 66.0 66.0 67.0 67.0 68.0 68.0 68.0 68.0 68.0 68.0 69.0 70.0 71.0 71.0 72.0 74.0 75.0

MTB > desc c8

Variable	N	Mean	Median	TrMean	StDev	SEMean
C8	33	66.197	66.000	66.052	3.865	0.673
Variable	Min	Max	Q1	Q3
C8	60.000	75.000	63.000	68.000

(a) Calculate a 95% confidence interval for m based on these data. Since we don't know the population standard deviation, substitute the sample standard deviation for now.

(b) What do you think is a reasonable definition for m?

(d) What proportion of the sample is this (your value in (c))? Should this proportion be close to 95%? Explain.