Question

7)A researcher wishes to​ estimate, with 99​% ​confidence, the population proportion of adults who think Congress is doing a good or excellent job. Her estimate must be accurate within

33​% of the true proportion.

​(a) No preliminary estimate is available. Find the minimum sample size needed.

​(b) Find the minimum sample size​ needed, using a prior study that found that

32​% of the respondents said they think Congress is doing a good or excellent job.

​(c) Compare the results from parts​ (a) and​ (b).

8) A researcher wishes to​ estimate, with 99​% ​confidence, the population proportion of adults who eat fast food four to six times per week. Her estimate must be accurate within

33​% of the population proportion.

​(a) No preliminary estimate is available. Find the minimum sample size needed.

​(b) Find the minimum sample size​ needed, using a prior study that found that

44​%

of the respondents said they eat fast food four to six times per week.

​(c) Compare the results from parts​ (a) and​ (b).

6) In a survey of 2327 ​adults,727 say they believe in UFOs.

Construct a 90% confidence interval for the population proportion of adults who believe in UFOs.

Answer 1

7)A researcher wishes to​ estimate, with 99​% ​confidence, the population proportion of adults who think Congress is doing a good or excellent job. Her estimate must be accurate within

33​% of the true proportion.

​(a) No preliminary estimate is available. Find the minimum sample size needed.

​(b) Find the minimum sample size​ needed, using a prior study that found that

32​% of the respondents said they think Congress is doing a good or excellent job.

​(c) Compare the results from parts​ (a) and​ (b).

a)

If we have not given a prior estimate we take p = 0.5 for unbiasedness.

Margin of error = E = 0.33

Confidence level = C = 0.99

Zc = 2.58   ( Using z table)

p = 0.50

We have to find sample size (n)

b)

Margin of error = E = 0.33

Confidence level = C = 0.99

Zc = 2.58    ( Using z table)

p = 0.32

We have to find sample size (n)

c)

If the prior estimator is not given then the sample size large as compare to given prior estimator.

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