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Chapter 8: Q66E (page 452)

Homework assistance for accounting students. Refer to the Journal of Accounting Education (Vol. 25, 2007) study of providing homework assistance to accounting students, Exercise 8.18 (p. 468). Recall that one group of students was given a completed homework solution and another group was given only check figures at various steps of the solution. The researchers wanted to compare the average test score improvement of the two groups. How many students should be sampled in each group to estimate the difference in the averages to within .5 point with 99% confidence? Assume that the standard deviations of the test score improvements for the two groups are approximately equal to 1

Short Answer

Expert verified

The required sample size is 54.

Step by step solution

01

Given Information

The standard deviation of two groups are given below

σ1=σ2=1

The sampling error is

SE=.5

02

Z-value

For α=0.01

The z-value is given by

zα2=z0.005=2.58

03

Compute the sample

For, z=2.58,σ1=σ2=1 andSE=.5

The sample is calculated as

n1=n2=z0.0052×σ12+σ22SE2=2.582×12+12.52=6.6564×2.25=13.3128.25=53.2512≈54

Therefore, the required sample size is 54.

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Most popular questions from this chapter

Assume that x is a binomial random variable with n = 1000 andp = 0.50. Use a normal approximation to find each of the following probabilities:

a. P(x>500)

b.P(490≤x<500)

c.P(x>550)

History of corporate acquisitions. Refer to the Academy of Management Journal (August 2008) investigation of the performance and timing of corporate acquisitions, Exercise 2.12 (p. 74). Recall that the investigation discovered that in a random sample of 2,778 firms, 748 announced one or more acquisitions during the year 2000. Does the sample provide sufficient evidence to indicate that the true percentage of all firms that announced one or more acquisitions during the year 2000 is less than 30%? Use a=0.05to make your decision.

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’ “rookie” 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 numberoftimesplayeron 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)=β0+β1x1+β2x2+β3x3+β4x4+β5x5+β6x6+β7x7+β8x8+β9x9+β10x10+β11x11+β12x12 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:β^1=-0.147,sβ^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’ rookie cards.
  3. Refer to part a. Statistics for the card vintage variable were reported as follows:β^3=-0.074,sβ^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’ 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.

Shared leadership in airplane crews. Refer to the Human Factors (March 2014) study of shared leadership by the cockpit and cabin crews of a commercial airplane, Exercise 8.14 (p. 466). Recall that each crew was rated as working either successfully or unsuccessfully as a team. Then, during a simulated flight, the number of leadership functions exhibited per minute was determined for each individual crew member. One objective was to compare the mean leadership scores for successful and unsuccessful teams. How many crew members would need to be sampled from successful and unsuccessful teams to estimate the difference in means to within .05 with 99% confidence? Assume you will sample twice as many members from successful teams as from unsuccessful teams. Also, assume that the variance of the leadership scores for both groups is approximately .04.

A random sample of n = 6 observations from a normal distribution resulted in the data shown in the table. Compute a 95% confidence interval for σ2
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