Confidence Interval and Margin of Error

What is the effect of increasing the sample size on the width of the confidence interval, assuming the confidence level remains the same?

• The width of the confidence interval increases.

• The width of the confidence interval decreases.

• The width of the confidence interval stays the same.

• The width of the confidence interval doubles.

What happens to the confidence interval if the standard deviation of the population decreases, assuming all other factors remain constant?

• The confidence interval becomes wider.

• The confidence interval becomes narrower.

• The confidence interval remains unchanged.

• The confidence interval inverts.

What can be inferred about the relationship between confidence level and margin of error?

• Increasing the confidence level decreases the margin of error.

• Increasing the confidence level increases the margin of error.

• The confidence level and margin of error are not related.

• Decreasing the confidence level decreases the margin of error.

What is the impact on the confidence interval if the confidence level is decreased from 99% to 95%, assuming all other factors remain constant?

• The confidence interval becomes wider.

• The confidence interval becomes narrower.

• There is no impact on the confidence interval.

• The confidence interval becomes twice as wide.

How does an increase in the population standard deviation from 5 to 10 affect the width of a 95% confidence interval, assuming the sample size and confidence level remain constant?

• The width of the confidence interval increases.

• The width of the confidence interval decreases.

• The width of the confidence interval remains unchanged.

• The width of the confidence interval is halved.

What effect does doubling the sample size have on the margin of error in a confidence interval, assuming the confidence level remains constant?

• The margin of error is cut in half.

• The margin of error remains the same.

• The margin of error doubles.

• The margin of error is reduced, but not cut in half.

Which is true about a 95% confidence interval?

I. There is a 95% chance that the parameter is in the calculated interval.

II. We're 95% confident that the statistic lies in the interval.

III. The interval is narrower than a 98% confidence interval.

• I only

• II only

• III only

• I and II only

• II and III only

For a class project, a student in a statistics class surveys the monthly rent for 32 unfurnished one-bedroom apartments in Boston and finds the mean monthly rent to be $1400 with a standard deviation of $220.

Find the margin of error for the sample mean. (assuming 95% confidence) Round to the nearest hundredth

• $77.78

• $4.31

• $188.78

• $494.97

A researcher wishes to estimate, within $25, the true mean amount of postage a community college spends each year. The standard deviation is known to be $80. If she wishes to be 95% confident in her estimate of the true mean amount of postage, how large a sample is necessary? Round to the nearest whole number

• 41

• 25

• 80

• 200

For a class project, a student in a statistics class surveys the monthly rent for 32 unfurnished one-bedroom apartments in Boston and finds the mean monthly rent to be $1400 with a standard deviation of $220.

Find the 95% confidence interval for the population mean Round to the nearest hundredth

• [1322.22, 1477.78]

• [1395.69, 1404.31]

• [1211.22, 1588.78]

• [905.03, 1894.97]