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Chapter 8: Q68E (page 452)

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?

Short Answer

Expert verified

The required sample size is 3383.

Step by step solution

01

Given Information

With a 95% confidence interval, a pollster intends to calculate the actual difference between the proportion of men and women.

From the given information

2SE=0.04SE=0.02
02

Z-value

For 伪=0.1

The z-value is given by

z伪2=z0.05=1.645

03

Compute the sample

For, z=1.645,p1=p2=0.5鈥�andSE=0.02

The sample is calculated as

n1=n2=z0.052脳p11-p1+p21-p2SE2=1.6452脳0.25+0.250.022=2.706025脳.50.0004=1.35301250.0004=3382.53鈮�3383

Therefore, the required sample size is 3383.

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Most popular questions from this chapter

4.111 Personnel dexterity tests. Personnel tests are designed to test a job applicant鈥檚 cognitive and/or physical abilities. The Wonderlic IQ test is an example of the former; the Purdue Pegboard speed test involving the arrangement of pegs on a peg board is an example of the latter. A particular

dexterity test is administered nationwide by a private testing service. It is known that for all tests administered last year, the distribution of scores was approximately normal with mean 75 and standard deviation 7.5.

a. A particular employer requires job candidates to score at least 80 on the dexterity test. Approximately what percentage of the test scores during the past year exceeded 80?

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Consider the discrete probability distribution shown here.

x

10

12

18

20

p

.2

.3

.1

.4

a. Calculate渭,蟽2 and蟽 .

b. What isP(x<15) ?

c. Calculate 渭卤2蟽 .

d. What is the probability that xis in the interval 渭卤2蟽 ?

Given the following values of x, s, and n, form a 90% confidence interval for蟽2

a. x=21,s=2.5,n=50

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Homework assistance for accounting students. How much assistance should accounting professors provide students for completing homework? Is too much assistance counterproductive? These were some of the questions of interest in a Journal of Accounting Education (Vol. 25, 2007) article. A total of 75 junior-level accounting majors who were enrolled in Intermediate Financial Accounting participated in an experiment. All students took a pretest on a topic not covered in class; then, each was given a homework problem to solve on the same topic. However, the students were randomly assigned different levels of assistance on the homework. Some (20 students) were given the completed solution, some (25 students) were given check figures at various steps of the solution, and the rest (30 students) were given no help. After finishing the homework, each student was given a posttest on the subject. One of the variables of interest to the researchers was the knowledge gain (or test score improvement), measured as the difference between the posttest and pretest scores. The sample means knowledge gains for the three groups of students are provided in the table.

a. The researchers theorized that as the level of homework assistance increased, the test score improvement from pretest to post test would decrease. Do the sample means reported in the table support this theory?

b. What is the problem with using only the sample means to make inferences about the population mean knowledge gains for the three groups of students?

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To compare the means of two populations, independent random samples of 400 observations are selected from each population, with the following results:

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Sample 2

x炉1=5,275蟽1=150

x炉2=5,240蟽2=200

a. Use a 95%confidence interval to estimate the difference between the population means (渭1鈭�渭2). Interpret the confidence interval.

b. Test the null hypothesis H0:(渭1鈭�渭2)=0versus the alternative hypothesis Ha:(渭1鈭�渭2)鈮�0 . Give the significance level of the test and interpret the result.

c. Suppose the test in part b was conducted with the alternative hypothesis Ha:(渭1鈭�渭2)鈮�0 . How would your answer to part b change?

d. Test the null hypothesis H0:(渭1鈭�渭2)=25 versus Ha:(渭1鈭�渭2)鈮�25. Give the significance level and interpret the result. Compare your answer with the test conducted in part b.

e. What assumptions are necessary to ensure the validity of the inferential procedures applied in parts a鈥揹?
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