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Chapter 7: Q.4 (page 460)

The central limit theorem is important in statistics because it allows us to use the Normal distribution to make inferences concerning the population mean

(a) if the sample size is reasonably large (for any population).

(b) if the population is normally distributed and the sample size is reasonably large.

(c) if the population is normally distributed (for any sample size).

(d) if the population is normally distributed and the population variance is known (for any sample size).

(e) if the population size is reasonably large (whether the population distribution is known or not,

Short Answer

Expert verified

The correct answer is (a) if the sample size is reasonably large (for any population).

Step by step solution

01

Given Information

The central limit theorem is important in statistics because it allows us to use the Normal distribution to make inferences concerning the population mean

02

Explanation

If the population distribution is not Normal, the central limit theorem (CLT) states that when nis large, the sampling distribution of x is approximately Normal.

We know that according to the central limit theorem if the sample size of a sampling distribution is 30or more; then the sampling distribution which has a sample mean x炉is approximately Normal.

Hence, the correct answer is (a).

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