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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铃�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铃�and the product of n and (1-p铃�)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铃�and the product of n and (1-width="11">p铃�) is shown below:

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

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Most popular questions from this chapter

If nothing is known about p, .5 can be substituted for p in the sample size formula for a population proportion. But when this is done, the resulting sample size may be larger than needed. Under what circumstances will be using p = .5 in the sample size formula yield a sample size larger than needed to construct a confidence interval for p with a specified bound and a specified confidence level?

Unethical corporate conduct. How complicit are entrylevel accountants in carrying out an unethical request from their superiors? This was the question of interest in a study published in the journal Behavioral Research in Accounting (July 2015). A sample of 86 accounting graduate students participated in the study. After asking the subjects to perform what is clearly an unethical task (e.g., to bribe a customer), the researchers measured each subject鈥檚 intention to comply with the unethical request score. Scores ranged from -1.5 (intention to resist the unethical request) to 2.5 (intention to comply with the unethical request). Summary statistics on the 86 scores follow: x炉=2.42,s=2.84.

a. Estimate 渭, the mean intention to comply score for the population of all entry-level accountants, using a 90% confidence interval.

b. Give a practical interpretation of the interval, part a.

c. Refer to part a. What proportion of all similarly constructed confidence intervals (in repeated sampling) will contain the true value of 渭?

d. Compute the interval, x炉卤2s. How does the interpretation of this interval differ from that of the confidence interval, part a?

Suppose N= 10,000, n= 2,000, and s= 50.

a. Compute the standard error of xusing the finite populationcorrection factor.

b. Repeat part a assuming n= 4,000.

c. Repeat part a assuming n= 10,000.

d. Compare parts a, b, and c and describe what happens to the standard error of xas nincreases.

e. The answer to part c is 0. This indicates that there is no sampling error in this case. Explain.

Surface roughness of pipe. Refer to the Anti-corrosion Methods and Materials (Vol. 50, 2003) study of the surface roughness of coated interior pipe used in oil fields, Exercise 2.46 (p. 96). The data (in micrometers) for sampled pipe sections are reproduced in the accompanying table; a Minitab analysis of the data appears below.

a.Locate a 95%confidence interval for the mean surface roughness of coated interior pipe on the accompanying Minitab printout.

b.Would you expect the average surface roughness to beas high as 2.5micrometres? Explain.

Products 鈥淢ade in the USA.鈥� Refer to Exercise 2.154 (p. 143) and the Journal of Global Business (Spring 2002) survey to determine what 鈥淢ade in the USA鈥� means to consumers. Recall that 106 shoppers at a shopping mall in Muncie, Indiana, responded to the question, 鈥淢ade in the USA鈥� means what percentage of U.S. labor and materials?鈥� Sixty-four shoppers answered,鈥�100%.鈥�

a. Define the population of interest in the survey.

b. What is the characteristic of interest in the population?

c. Estimate the true proportion of consumers who believe 鈥淢ade in the USA鈥� means 100% U.S. labor and materials using a 90% confidence interval.

d. Give a practical interpretation of the interval, part c.

e. Explain what the phrase 鈥�90% confidence鈥� means for this interval.

f. Compute the sample size necessary to estimate the true proportion to within .05 using a 90% confidence interval.
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