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Chapter 7: Q 36. (page 462)

Male workers A factory employs 3000unionized workers, 90%of whom are male. A random sample of 15 workers is selected for a survey about worker satisfaction. Let p^= the proportion of males in the sample.

a. Identify the mean of the sampling distribution of p^

b. Calculate and interpret the standard deviation of the sampling distribution of p^.

Verify that the 10%condition is met.

c. Describe the shape of the sampling distribution of p^. Justify your answer.

Short Answer

Expert verified

a. Mean of sampling distribution is 0.90

b. Standard deviation is 0.0775.

c. Shape is skewed to left.

Step by step solution

01

Given Information

It is given that p=90%=0.90

n=15

02

Mean of sampling distribution

The mean is渭p^=p=90%=0.90

03

Standard Deviation

We know that standard deviation is:

蟽p^=p(1-p)n

=0.90(1-0.90)15

=0.0775

The standard deviation is role="math" localid="1654889468124" 0.0775

04

Shape of sampling distribution

Condition of normality is np鈮�10andn(1-p)鈮�10

Here, np=15(0.90)=13.5鈮�10

n(1-n)=15(1-0.90)=1.5<10

Population proportion is 0.90which is closer to 1. Hence, sampling distribution is skewed to left.

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