Chapter 8 Homework Questions

It is known that the population is not normally distributed. Also, the population standard deviation is not known. A sample of 6 items is selected from this population to develop an interval estimate for the mean of the population (µ). Choose the correct alternative below.

The sample size must be increased for constructing the confidence interval.

In order to construct an interval estimate for the population mean when σ is known and the sample is very small, the population

must have a normal distribution

For the interval estimation of µ when σ is known and the sample is large, the proper distribution to use is

standard normal distrbution

For a given confidence level and sample size, which of the following is true in the interval estimation of the population mean when σ is known?

If the population standard deviation is greater, the interval is wider.

After computing a confidence interval, the user believes the results are meaningless because the width of the interval is too large. Which one of the following is the best recommendation?

Increase the sample size

Given that a 95% confidence interval is (6.5, 12.5), we can state that

We expect that 95% of all possible sample means drawn from the population will produce confidence intervals that include the population's mean (which makes us 95% confident that interval (6.5, 12.5) contains the population mean)

A 95% confidence interval for the population mean is determined to be between 100 and 120. If the confidence level is reduced to 90%, the confidence interval for µ

becomes narrower

As the number of degrees of freedom for the t distribution increases, the difference between the t distribution and the standard normal distribution

becomes smaller

As the sample size increases, the margin of error

decreases