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Chapter 8: Q 32E (page 479)

Question: Performance ratings of government agencies. The U.S. Office of Management and Budget (OMB) requires government agencies to produce annual performance and accounting reports (PARS) each year. A research team at George Mason University evaluated the quality of the PARS for 24 government agencies (The Public Manager, Summer 2008), where evaluation scores ranged from 12 (lowest) to 60 (highest). The accompanying file contains evaluation scores for all 24 agencies for two consecutive years. (See Exercise 2.131, p. 132.) Data for a random sample of five of these agencies are shown in the accompanying table. Suppose you want to conduct a paired difference test to determine whether the true mean evaluation score of government agencies in year 2 exceeds the true mean evaluation score in year 1.

Source: J. Ellig and H. Wray, “Measuring Performance Reporting Quality,” The Public Manager, Vol. 37, No. 2, Summer 2008 (p. 66). Copyright © 2008 by Jerry Ellig. Used by permission of Jerry Ellig.

a. Explain why the data should be analyzedusing a paired difference test.

b. Compute the difference between the year 2 score and the year 1 score for each sampled agency.

c. Find the mean and standard deviation of the differences, part

b. Use the summary statistics, part c, to find the test statistic.

e. Give the rejection region for the test using a = .10.

f. Make the appropriate conclusion in the words of the problem.

Short Answer

Expert verified

  1. The paired t-test is a technique for determining whether or not the mean difference between two values is zero. Since the two samples contain similar individuals, their names indicate that they are paired and reliant.

  2. Year 1 and year 2 score is (-6, -2,0, -10, -15)

  3. 6.0663

  4. -2.43279

  5. 4

  6. The mean genuine evaluation score in the first year.

Step by step solution

01

(a) Paired t-test

When we are concerned with the contrast among two variables for similar participants as well as data obtained from the identical pair of organizations, we utilize the paired - t-test.

02

(b) Difference between Year 2 and Year 1 score

03

(c) Mean of the difference

04

(d) Use test statistics

Null Hypothesis: µd = 0

Alternative Hypothesis: µd < 0

05

(e) Rejection region for the test

06

(f) Conclusion

With the t-score, ( -2.43279 ) < - 1.533 we can reject the null hypothesis at 0. I significance level as well as conclude that there is enough proof to demonstrate that the accurate mean score of evaluation authority agencies in 2008 exceeds the mean genuine evaluation score in 2007

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Most popular questions from this chapter

Traffic sign maintenance. Refer to the Journal of Transportation Engineering (June 2013) study of traffic sign maintenance in North Carolina, Exercise 8.54 (p. 489). Recall that the proportion of signs on NCDOT-maintained roads that fail minimum requirements was compared to the corresponding proportion for signs on county-owned roads. How many signs should be sampled from each maintainer to estimate the difference between the proportions to within .03 using a 90% confidence interval? Assume the same number of signs will be sampled from NCDOT-maintained roads and county-owned roads

Find a value of the standard normal random variable z, call it z0, such that

a.P(z≤z0)=0.2090b.P(z≤z0)=0.7090c.P(-z0≤z<z0)=0.8472d.P(-z0≤z<z0)=0.1664e.P(z0≤z≤z0)=0.4798f.P(-1<z<z0)

Consider the discrete probability distribution shown here.

x

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12

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20

p

.2

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Comparing taste-test rating protocols. Taste-testers of new food products are presented with several competing food samples and asked to rate the taste of each on a 9-point scale (where1="dislike extremely" and9="like extremely"). In the Journal of Sensory Studies (June 2014), food scientists compared two different taste-testing protocols. The sequential monadic (SM) method presented the samples one-at-a-time to the taster in a random order, while the rank rating (RR) method presented the samples to the taster all at once, side-by-side. Consider the following experiment (similar to the one conducted in the journal): 50 consumers of apricot jelly were asked to taste test five different varieties. Half the testers used the SM protocol and half used the RR protocol during testing. In a second experiment, 50 consumers of cheese were asked to taste-test four different varieties. Again, half the testers used the SM protocol and half used the RR protocol during testing. For each product (apricot jelly and cheese), the mean taste scores of the two protocols (SM and RR) were compared. The results are shown in the accompanying tables.

a. Consider the five varieties of apricot jelly. Identify the varieties for which you can conclude that "the mean taste scores of the two protocols (SM and RR) differ significantly atα=.05."

b. Consider the four varieties of cheese. Identify the varieties for which you can conclude that "the mean taste scores of the two protocols (SM and RR) differ significantly atα=.05."

c. Explain why the taste-test scores do not need to be normally distributed for the inferences, parts a and b, to be valid.

Ages of self-employed immigrants. Is self-employment for immigrant workers a faster route to economic advancement in the country? This was one of the questions studied in research published in the International Journal of Manpower (Vol. 32, 2011). One aspect of the study involved comparing the ages of self-employed and wage-earning immigrants. The researcher found that in Sweden, native wage earners tend to be younger than self-employed natives. However, immigrant wage earners tend to be older than self-employed immigrants. This inference was based on the table's summary statistics for male Swedish immigrants.

Self-employed immigrants

Wage-earning immigrants

Sample Size

870

84,875

Mean

44.88

46.79

Source: Based on L. Andersson, "Occupational Choice and Returns to Self-Employment Among Immigrants," International Journal of Manpower, Vol. 32, No. 8, 2011 (Table I).

a. Based on the information given, why is it impossible to provide a measure of reliability for the inference "Self-employed immigrants are younger, on average, than wage-earning immigrants in Sweden"?

b. What information do you need to measure reliability for the inference, part a?

c. Give a value of the test statistic that would conclude that the true mean age of self-employed immigrants is less than the true mean age of wage-earning immigrants if you are willing to risk a Type I error rate of .01.

d. Assume that s, the standard deviation of the ages is the same for both self-employed and wage-earning immigrants. Give an estimate of s that would lead you to conclude that the true mean age of self-employed immigrants is less than the true mean age of wage-earning immigrants using α=0.01 .

e. Is the true value of s likely to be larger or smaller than the one you calculated in part d?
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