Sample Size of Confidence Intervals

A population has a standard deviation of σ = 17.3. How large of a sample must be drawn so that a 95% confidence interval for µ will have a Margin of Error equal to 1.4?

• 586.6

• 587

• 586

• 585

The lifetime of a certain type of batter is known to be normally distributed with a standard deviation of 20 hours. A sample of 50 batteries had a mean lifetime of 120.1 hours. It is desired to construct a 99% confidence interval for the mean lifetime of this type of battery.

What is the Confidence Interval to one decimal place?

• (114.5, 125.6)

• (112.8, 127.4)

• (112.82, 127.38)

• (114.56, 125.64)

A person selects a random sample of 15 credit cards and determines the annual interest rate, in percent, of each one. The sample mean is 12.42 with a sample standard deviation of 1.3. It is desired to construct a 90% Confidence Interval.

Find the Standard Error to three decimal places.

• 0.336

• 0.33566

• 13.156

• 0.087

A quality control inspector will measure the salt content (in milligrams) in a random sample of bags of potato chips from an hour of production. Which of the following would result in the smallest margin of error in estimating the mean salt content μ?

• 90% confidence; n = 25

• 90% confidence; n = 50

• 95% confidence; n = 25

• 95% confidence; n = 50

• n=100 at any confidence level

A research group wishes to estimate the mean amount of time (in hours) that members of a fitness center spend exercising each week. They want to estimate the mean within a margin of error of 0.5 hours with a 95% level of confidence. Previous data suggests that the standard deviation of the population is 2.2. Which of the following is the smallest sample size they could use?

• 60

• 75

• 90

• 180

Which of the following would result in a smaller minimum sample size?

• Increasing the confidence level

• Not having a preliminary estimate for p-hat

• Decreasing the confidence level

• Decreasing the margin of error

A research group wishes to estimate the mean amount of time (in hours) that members of a fitness center spend exercising each week. They want to estimate the mean within a margin of error of 0.5 hours with a 95% level of confidence. Previous data suggests that the standard deviation of the population is 2.2. Which of the following is the smallest sample size they could use?

• 60

• 75

• 90

• 180

In a recent poll of 803 randomly selected baseball fans in Connecticut, 44% said their favorite team was the Yankees. If researchers wanted to reduce the margin of error to at most 2%, how many baseball fans do they have to randomly select? Use 95% confidence

• 1564

• 2367

• 803

• 3170

To achieve a narrower confidence interval for a given confidence level, one should:

• Increase the sample size.

• Decrease the sample size.

• Increase the standard deviation.

• Decrease the confidence level.

What happens to the margin of error if the sample size is quadrupled, all else being equal?

• It is halved.

• It is doubled.

• It remains the same.

• It is quadrupled.