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Chapter 6: Q-41E (page 356)

Question: For the binomial sample information summarized in each part, indicate whether the sample size is large enough to use the methods of this chapter to construct a confidence interval for p.

a. n = 400,p^= .10

b. n = 50,p^= .10

c. n = 20,p^= .5

d. n = 20,p^= .3

Short Answer

Expert verified

Answer

  1. Large
  2. Not large
  3. Not large
  4. Not large

Step by step solution

01

Determining whether the sample size is large when n is 400 and p⏞ is 0.10

a.Theproductofnandp⏞andtheproductofnand(1-)isshownbelow:

As both the values are above 15, the sample size is quite large.

02

Determining whether the sample size is large when n is 50 and p⏜is 0.10


The product of n and p⏞and the product of n and (1-p⏞)is shown below:

As one of the values is not above 15, the sample size is not large.

03

Determining whether the sample size is large when n is 20 and p^ is 0.5

c.

The product of n and and the product of n and (1-) is shown below:

As both the values are not above 15, the sample size is not large.

04

Determining whether the sample size is large when n is 20 and p⏞ is 0.3

d.

The product of n and p⏞and the product of n and (1-width="11">p⏜) is shown below:

As both the values are not above 15, the sample size is not large.

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Employees with substance abuse problems. According to the New Jersey Governor’s Council for a Drug-Free Workplace Report, 50 of the 72 sampled businesses that are members of the council admitted that they had employees with substance abuse problems. At the time of the survey, 251 New Jersey businesses were members of the Governor’s Council. Use the finite population correction factor to find a 95% confidence interval for the proportion of all New Jersey Governor’s Council business members who have employees with substance abuse problems. Interpret the resulting interval.

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