Margin of Error and Sample Size

The principal of a large high school wanted to know how many hours students spend doing homework during a typical week. Based on a random sample of 100 students, a 90% confidence interval for the mean number of hours doing homework for all students is 2.3 hours to 4.1 hours. Explain what would happen to the length of the interval if the sample size were increased to 200 students.

• The length of the interval would be narrower, because increasing the sample size decreases the margin of error.

• The length of the interval would be wider, because increasing the sample size decreases the margin of error.

• The length of the interval would be narrower, because decreasing the sample size increases the margin of error.

• The length of the interval would be wider, because decreasing the sample size increases the margin of error.

The puzzle editor of a game magazine asked 43 randomly selected subscribers how long it took them to complete a certain crossword puzzle. The 99% confidence interval for the median completion time for all subscribers is 15.2 to 18.6 minutes. Explain what would happen to the length of the interval if the confidence level were decreased to 90%.

• The length of the interval would be narrower, because decreasing the confidence level decreases the margin of error.

• The length of the interval would be wider, because decreasing the confidence level decreases the margin of error.

• The length of the interval would be narrower, because increasing the confidence level decreases the margin of error.

• The length of the interval would be wider, because increasing the confidence level increases the margin of error.

A New York Times/CBS News poll asked a random sample of U.S. adults, "Do you favor an amendment to the Constitution that would permit organized prayer in public schools?" Based on this poll, the 95% confidence interval for the proportion of all U.S. adults who favor such an amendment is 0.63 to 0.69. Explain what would happen to the length of the interval if the confidence level were decreased to 90%

• The length of the interval would be narrower, because decreasing the confidence level decreases the margin of error.

• The length of the interval would be wider, because decreasing the confidence level decreases the margin of error.

• The length of the interval would be narrower, because increasing the confidence level increases the margin of error.

• The length of the interval would be wider, because increasing the confidence level increases the margin of error.

A Gallup poll asked a random sample of U.S. adults, "Would you like to lose weight?" Based on this poll, the 95% confidence interval for the proportion of all U.S. adults who want to lose weight is 0.56 to 0.62. Explain what would happen to the length of the interval if the confidence level were increased to 99%.

• The length of the interval would be wider, because increasing the confidence level increases the margin of error.

• The length of the interval would be narrower, because increasing the confidence level increases the margin of error.

• The length of the interval would be narrower, because decreasing the confidence level decreases the margin of error.

• The length of the interval would be wider, because decreasing the confidence level increases the margin of error.

The principal of a large high school wanted to know how many hours students spend doing homework during a typical week. Based on a random sample of 100 students, a 90% confidence interval for the mean number of hours doing homework for all students is 2.3 hours to 4.1 hours. Explain what would happen to the length of the interval if the confidence level were increased to 99%.

• The length of the interval would be narrower, because increasing the confidence level decreases the margin of error.

• The length of the interval would be wider, because increasing the confidence level increases the margin of error.

• The length of the interval would be narrower, because decreasing the confidence interval increases the margin of error.

• The length of the interval would be wider, because decreasing the confidence interval increases the margin of error.

The puzzle editor of a game magazine asked 43 randomly selected subscribers how long it took them to complete a certain crossword puzzle. The 99% confidence interval for the median completion time for all subscribers is 15.2 to 18.6 minutes. Explain what would happen to the length of the interval if the sample size were increased to 100.

• The length of the interval would be narrower, because increasing the sample size decreases the margin of error.

• The length of the interval would be wider, because decreasing the sample size increases the margin of error.

• The length of the interval would be wider, because increasing the sample size decreases the margin of error.

• The length of the interval would be wider, because decreasing the sample size decreases the margin of error.

A New York Times/CBS News poll asked a random sample of U.S. adults, "Do you favor an amendment to the Constitution that would permit organized prayer in public schools?" Based on this poll, the 95% confidence interval for the proportion of all U.S. adults who favor such an amendment is 0.63 to 0.69. Explain what would happen to the length of the interval if the sample size was only half as big as in the actual study.

• The length of the interval would be wider, because decreasing the sample size increases the margin of error.

• The length of the interval would be wider, because decreasing the sample size decreases the margin of error.

• The length of the interval would be narrower, because increasing the sample size increases the margin of error.

• The length of the interval would be narrower, because increasing the sample size decreases the margin of error.

A Gallup poll asked a random sample of U.S. adults, "Would you like to lose weight?" Based on this poll, the 95% confidence interval for the proportion of all U.S. adults who want to lose weight is 0.56 to 0.62. Explain what would happen to the length of the interval if the sample size was only half as big as in the actual study.

• The length of the interval would be wider, because increasing the sample size increases the margin of error.

• The length of the interval would be narrower, because increasing the sample size increases the margin of error.

• The length of the interval would be narrower, because decreasing the sample size decreases the margin of error.

• The length of the interval would be wider, because decreasing the sample size increases the margin of error.