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Chapter 5: Q56SE (page 322)

Question:A random sample of n = 500 observations is selected from a binomial population with p = .35.

a. Give the mean and standard deviation of the (repeated) sampling distribution ofp^the sample proportion of successes for the 500 observations.

b. Describe the shape of the sampling distribution of p^. Does your answer depend on the sample size?

Short Answer

Expert verified
  1. The mean and standard deviation of p^are .35 and 0.021.
  2. The answer depends on the sample size.

Step by step solution

01

Given Information

The sample size is 500.

The probability of success p=0.35

02

(a) Compute the mean and standard deviation

The mean of the sampling distribution of p^is given byp^=0.35

The standard deviation of the sampling distribution of is given byd=pqn=0.35×0.65500=0.021

03

Describing the shape of the p^

The sampling distribution of is normal as we know that if n is large, then the sampling distribution of follows the normal distribution with a mean p^and standard deviation

p1-pn

Therefore, the shape of the sampling distributionp^ isnormal.

Here, the number of samples is 500, which is greater than 30.

Therefore, the answer depends on the sample size.

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