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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, 鈥淢easuring Performance Reporting Quality,鈥� The Public Manager, Vol. 37, No. 2, Summer 2008 (p. 66). Copyright 漏 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: 碌d = 0

Alternative Hypothesis: 碌d < 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

The gender diversity of a large corporation鈥檚 board of directors was studied in Accounting & Finance (December 2015). In particular, the researchers wanted to know whether firms with a nominating committee would appoint more female directors than firms without a nominating committee. One of the key variables measured at each corporation was the percentage of female board directors. In a sample of 491firms with a nominating committee, the mean percentage was 7.5%; in an independent sample of 501firms without a nominating committee, the mean percentage was role="math" localid="1652702402701" 4.3% .

a. To answer the research question, the researchers compared the mean percentage of female board directors at firms with a nominating committee with the corresponding percentage at firms without a nominating committee using an independent samples test. Set up the null and alternative hypotheses for this test.

b. The test statistic was reported as z=5.1 with a corresponding p-value of 0.0001. Interpret this result if 伪=0.05.

c. Do the population percentages for each type of firm need to be normally distributed for the inference, part b, to be valid? Why or why not?

d. To assess the practical significance of the test, part b, construct a 95% confidence interval for the difference between the true mean percentages at firms with and without a nominating committee. Interpret the result.

Question: Impact of race on football card values. Refer to the Electronic Journal of Sociology (2007) study of the Impact of race on the value of professional football players鈥� 鈥渞ookie鈥� cards, Exercise 12.72 (p. 756). Recall that the sample consisted of 148 rookie cards of NFL players who were inducted into the Football Hall of Fame (HOF). The researchers modelled the natural logarithm of card price (y) as a function of the following independent variables:

Race:x1=1ifblack,0ifwhiteCardavailability:x2=1ifhigh,0iflowCardvintage:x3=yearcardprintedFinalist:x4=naturallogarithmof鈥�numberoftimesplayeron鈥�finalHOFballotPosition-QB::x5=1ifquarterback,0ifnotPosition-RB:x7=1ifrunningback,0ifnotPosition-WR:x8=1ifwidereceiver,0ifnotPosition-TEx9=1iftightend,0ifnotPosition-DL:x10=1ifdefensivelineman,0ifnotPosition-LB:x11=1iflinebacker,0ifnotPosition-DB:x12=1ifdefensiveback,0ifnot

[Note: For position, offensive lineman is the base level.]

  1. The model E(y)=尾0+尾1x1+尾2x2+尾3x3+尾4x4+尾5x5+尾6x6+尾7x7+尾8x8+尾9x9+尾10x10+尾11x11+尾12x12 was fit to the data with the following results:R2=0.705,Ra2=0.681,F=26.9.Interpret the results, practically. Make an inference about the overall adequacy of the model.
  2. Refer to part a. Statistics for the race variable were reported as follows:尾^1=-0.147,s尾^1=-0.145,t=-1.014,p-value=0.312 .Use this information to make an inference about the impact of race on the value of professional football players鈥� rookie cards.
  3. Refer to part a. Statistics for the card vintage variable were reported as follows:尾^3=-0.074,s尾^3=0.007,t=-10.92,p-value=.000.Use this information to make an inference about the impact of card vintage on the value of professional football players鈥� rookie cards.
  4. Write a first-order model for E(y) as a function of card vintage x3and position x5-x12that allows for the relationship between price and vintage to vary depending on position.

In a random sample of 250 people from a city, 148 of them favor apples over other fruits.

a. Use a 90% confidence interval to estimate the true proportion p of people in the population who favor apples over other fruits.

b. How large a sample would be needed to estimate p to be within .15 with 90% confidence?

Question: Deferred tax allowance study. A study was conducted to identify accounting choice variables that influence a manager鈥檚 decision to change the level of the deferred tax asset allowance at the firm (The Engineering Economist, January/February 2004). Data were collected for a sample of 329 firms that reported deferred tax assets in 2000. The dependent variable of interest (DTVA) is measured as the change in the deferred tax asset valuation allowance divided by the deferred tax asset. The independent variables used as predictors of DTVA are listed as follows:

LEVERAGE: x1= ratio of debt book value to shareholder鈥檚 equity

BONUS: x2 = 1 if firm maintains a management bonus plan,

0 if not

MVALUE: x3 = market value of common stock

BBATH: x4 = 1 if operating earnings negative and lower than last year,

0 if not

EARN: x5 = change in operating earnings divided by total assets

A first-order model was fit to the data with the following results (p-values in parentheses):

Ra2 = .280

y^=0.044+0.006x1-0.035x2-0.001x3+0.296x4+0.010x5

(.070) (.228) (.157) (.678) (.001) (.869)

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  3. Interpret the value of Ra2.

Forensic analysis of JFK assassination bullets. Following theassassination of President John F. Kennedy (JFK) in 1963, the House Select Committee on Assassinations (HSCA) conducted an official government investigation. The HSCA concluded that although there was a probable conspiracy involving at least one shooter in addition to Lee Harvey Oswald, the additional shooter missed all limousine occupants. A recent analysis of assassination bullet fragments, reported in the Annals of Applied Statistics(Vol. 1, 2007), contradicted these findings, concluding that the evidence used by the HSCA to rule out a second assassin is fundamentally flawed. It is well documented that at least two different bullets were the source of bullet fragments found after the assassination. Let E= {bullet evidence used by the HSCA}, T= {two bullets used in the assassination}, and= {more than two bullets used in the assassination}. Given the evidence (E), which is more likely to have occurred鈥� two bullets used (T) or more than two bullets used ?

a. The researchers demonstrated that the ratio,P(T\E)/P(Tc\E), is less than 1. Explain why this result supports the theory of more than two bullets used in the assassination of JFK.

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