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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

蟽1=蟽2=1

The sampling error is

SE=.5

02

Z-value

For 伪=0.01

The z-value is given by

z伪2=z0.005=2.58

03

Compute the sample

For, z=2.58,蟽1=蟽2=1鈥�andSE=.5

The sample is calculated as

n1=n2=z0.0052脳蟽12+蟽22SE2=2.582脳12+12.52=6.6564脳2.25=13.3128.25=53.2512鈮�54

Therefore, the required sample size is 54.

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Most popular questions from this chapter

Question: Refer to the Bulletin of Marine Science (April 2010) study of lobster trap placement, Exercise 6.29 (p. 348). Recall that the variable of interest was the average distance separating traps鈥攃alled trap-spacing鈥攄eployed by teams of fishermen. The trap-spacing measurements (in meters) for a sample of seven teams from the Bahia Tortugas (BT) fishing cooperative are repeated in the table. In addition, trap-spacing measurements for eight teams from the Punta Abreojos (PA) fishing cooperative are listed. For this problem, we are interested in comparing the mean trap-spacing measurements of the two fishing cooperatives.

BT Cooperative

93

99

105

94

82

70

86

PA Cooperative

118

94

106

72

90

66

98


Source: Based on G. G. Chester, 鈥淓xplaining Catch Variation Among Baja California Lobster Fishers Through Spatial Analysis of Trap-Placement Decisions,鈥� Bulletin of Marine Science, Vol. 86, No. 2, April 2010 (Table 1).

a. Identify the target parameter for this study.b. Compute a point estimate of the target parameter.c. What is the problem with using the normal (z) statistic to find a confidence interval for the target parameter?d. Find aconfidence interval for the target parameter.e. Use the interval, part d, to make a statement about the difference in mean trap-spacing measurements of the two fishing cooperatives.f. What conditions must be satisfied for the inference, part e, to be valid?

Conducting a political poll. A pollster wants to estimate the difference between the proportions of men and women who favor a particular national candidate using a 90% confidence interval of width .04. Suppose the pollster has no prior information about the proportions. If equal numbers of men and women are to be polled, how large should the sample sizes be?

Identify the rejection region for each of the following cases. Assume

v1=7andv2=9

a. Ha:蟽12&濒迟;蟽22,伪=.05

b. Ha:蟽12&驳迟;蟽22,伪=.01

c. Ha:蟽12鈮�蟽22,伪=.1withs12>s22

d. Ha:蟽12&濒迟;蟽22,伪=.025

Optimal goal target in soccer. When attempting to score a goal in soccer, where should you aim your shot? Should you aim for a goalpost (as some soccer coaches teach), the middle of the goal, or some other target? To answer these questions, Chance (Fall 2009) utilized the normal probability distribution. Suppose the accuracy x of a professional soccer player鈥檚 shots follows a normal distribution with a mean of 0 feet and a standard deviation of 3 feet. (For example, if the player hits his target,x=0; if he misses his target 2 feet to the right, x=2; and if he misses 1 foot to the left,x=-1.) Now, a regulation soccer goal is 24 feet wide. Assume that a goalkeeper will stop (save) all shots within 9 feet of where he is standing; all other shots on goal will score. Consider a goalkeeper who stands in the middle of the goal.

a. If the player aims for the right goalpost, what is the probability that he will score?

b. If the player aims for the center of the goal, what is the probability that he will score?

c. If the player aims for halfway between the right goal post and the outer limit of the goalkeeper鈥檚 reach, what is the probability that he will score?

Given that xis a hypergeometric random variable, computep(x)for each of the following cases:

a. N= 8, n= 5, r= 3, x= 2

b. N= 6, n= 2, r= 2, x= 2

c. N= 5, n= 4, r= 4, x= 3
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