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Chapter 8: Q 8.38 (page 331)

Assume that the population standard deviation is known and decide weather use of the z-interval procedure to obtain a confidence interval for the population mean is reasonable. Explain your answers

The distribution of the variable under consideration is highly skewed, and the sample size is 20.

Short Answer

Expert verified

The use of zinterval procedure to obtain a confidence interval for the population mean is not reasonable.

Step by step solution

01

Given Information

Sample size is 20.

The distribution of the variable under consideration is highly skewed.

02

Conditions to use z interval procedure

The conditions are:

  • Small Sample Size: When sample size is n<15, procedure is used if the variable is normally distributed and very close to being normally distributed.
  • Moderate Sample Size: When sample size is between 15-30, the variable is far from being normally distributed and no outlier in the data.
  • Large Sample Size: When the sample size is greater than 30, it is used without restrictions.
03

Explanation

Since the distribution of the variable under consideration is highly skewed and sample size is20, the use of z interval procedure to obtain a confidence interval for the population mean is not reasonable.

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Most popular questions from this chapter

We provide a sample mean, sample size, and population standard deviation. In each case, perform the following tasks.

a. Find a 95% confidence interval for the popularion mean. (Note: You may want to review Example 8.2, which begins on page 316.)

b. Identify and interpret the margin of error:

c. Express the endpoints of the confidence interval in terms of the point estimate and the margin of error.

where, x^=20,n=36,σ=3

Explain the difference between a point estimate of a parameter and a confidence-interval estimate of a parameter.

Assume that the population standard deviation is known and decide weather use of the zinterval procedure to obtain a confidence interval for the population mean is reasonable. Explain your answers.

The variable under consideration is very close to being normally distributed, and the sample size is75.

Assume that the population standard deviation is known and decide weather use of the z-interval procedure to obtain a confidence interval for the population mean is reasonable. Explain your answers.

The variable under consideration is very close to being normally distributed, and the sample size is 10.

What is meant by saying that a 1-αconfidence interval is

a. exact?

b. approximately correct?
See all solutions

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