Definition Questions 1 As confidence level increases the wid

Definition Questions:

1. As confidence level increases, the width of a confidence interval ____________.

increases.

decreases.

remains the same.

2. As variability of the characteristic being measured increases (in other words, as population standard deviation increases), the width of a confidence interval _____________.

increases.

decreases.

remains the same.

3. The law of large numbers states that as sample size increases, the sample mean

gets larger and larger.

gets smaller and smaller.

gets closer and closer to the population mean.

4. What effect does increasing the sample size have on the spread of the sampling distribution of x-bar?

The spread of the sampling distribution gets closer to the spread of the population.

The spread of the sampling distribution gets larger.

The spread of the sampling distribution gets smaller.

It has no effect. The spread of the sampling distribution always equals the spread of the population.

5. A sample is taken and a confidence interval for the population mean is found. If you decided you wanted a smaller margin of error for your interval, which of the following would result in a smaller margin of error?

Use a larger confidence level.

Use a larger sample size.

Use a larger value for the population standard deviation.

Use a larger value for the sample standard deviation.

Solution

1) Width of confidence level increases (as 1.64 becomes 1.96 thus increasing width)

2) As std deviation increasing margin of error z*sigma/rtn increases hence

Width of confidence level increases

3)

gets closer and closer to the population mean.

as Margin of error becomes very less.

4) The spread of the sampling distribution gets closer to the spread of the population.

5) Use a larger sample size.