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Chapter 6: Q50 (page 357)

Question: Nannies who are INA certified. The International Nanny Association (INA) reports that in a sample of 928 in-home child care providers (nannies), 128 have passed the INA Nanny Credential Exam (2014 International Nanny Association Salary and Benefits Survey). Use Wilson鈥檚 adjustment to find a 95% confidence interval for the true proportion of all nannies who have passed the INA certification exam.

Short Answer

Expert verified

We are 95% confident that the true proportion of all nannies that have passed the INA certification exam lies between the interval of 0.117 and 0.161.

Step by step solution

01

Given Information

The sample size was n=928.

The number of successes in the sample, x=128.

The confidence interval=95%.

02

Compute the adjusted sample proportion

The adjusted population proportion is calculated as:

p~=x+2n+4=128+2928+4=0.139

03

Compute the confidence interval of p

The significance level corresponds to the 95% confidence interval is,

1-伪=0.95伪=0.05

The value of is obtained from the standard normal table is,

Z伪2=Z0.025=1.96

The 95% confidence interval for the proportion is computed as

C.I=p~卤Z伪2p~1-p~n+4=0.139卤1.96脳0.1391-0.139928+4=0.139卤0.022=0.117,0.161

Hence, we are 95% confident that the actual proportion of all nannies that have passed the INA certification exam lies between the interval of 0.117 and 0.161.

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Most popular questions from this chapter

It costs you \(10 to draw a sample of size n = 1 and measure the attribute of interest. You have a budget of \)1,500.

a. Do you have sufficient funds to estimate the population mean for the attribute of interest with a 95% confidence interval 5 units in width? Assume蟽=14.

b. If you used a 90% confidence level, would your answer to part a change? Explain.

FindZ伪/2for each of the following:

a.= .10

b.= .01

c.= .05

d.= .20

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?

Question: Is Starbucks coffee overpriced? The Minneapolis Star Tribune (August 12, 2008) reported that 73% of Americans say that Starbucks coffee is overpriced. The source of this information was a national telephone survey of 1,000 American adults conducted by Rasmussen Reports.

a. Identify the population of interest in this study.

b. Identify the sample for the study.

c. Identify the parameter of interest in the study.

d. Find and interpret a 95% confidence interval for the parameter of interest.

Corporate sustainability of CPA firms. Refer to the Business and Society (March 2011) study on the sustainability behaviors of CPA corporations, Exercise 6.12 (p. 339). Recall that the level of support for corporate sustainability (measured on a quantitative scale ranging from 0 to 160 points) was obtained for each in a sample of 992 senior managers at CPA firms. The accompanying Minitab printout gives 90% confidence intervals for both the variance and standard deviation of level of support for all senior managers at CPA firms.

a. Locate the 90% confidence interval for 蟽2on the printout. Interpret the result. b. Use the sample variance on the printout to calculate the 90% confidence interval for蟽2. Does your result agree with the interval shown on the printout?

c. Locate the 90% confidence interval for on the printout.

d. Use the result, part a, to calculate the 90% confidence interval for蟽. Does your result agree with the interval shown on the printout?

e. Give a practical interpretation of the 90% confidence interval for.蟽

f. What assumption about the distribution of level of support is required for the inference, part e, to be valid? Is this assumption reasonably satisfied? (Use your answer to Exercise 4.125, p. 270.)
See all solutions

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