Section 15

A sample of 20 cupcakes found the interval for average calories to be (150, 350). Which is the correct interpretation of the 95% confidence interval?

• We are 95% confident that the true mean caloric content can be found with a sample of 150 to 350 cupcakes.

• We are 95% confident that the interval (150, 350) captures the true average caloric content.

• We are 95% confident that a sample of 20 cupcakes will find 250 calories per cupcake.

• None of these are correct.

The amount added and subtracted to the statistic.

• Margin of Error

• Point Estimator

• Statistic

• Population

A research company wants to estimate the proportion of people who like oatmeal.  They want the confidence level to be 95%.  The company gets 325 people to sign up for the survey, but on the day that the survey is issued, only 250 people show up and take the survey.  What happens to the confidence interval?

• It gets larger
• It gets smaller
• It stays the same
• Too little information given

Increasing the sample size __________ the confidence interval. 

• increases
• decreases
• does not affect
• there is not enough evidence to determine the answer

What can you do to reduce the margin of error? 

• increase the confidence level
• decrease the confidence level
• increase sample size
• decrease sample size

A 90% confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. The interval was ($139,048, $154,144). Give a practical interpretation of the interval.

• 90% of the sampled CEOs have salaries that fell in the interval $139,048 to $154,144
• We are 90% confident that the mean salary of all CEOs in the electronics industry falls in the interval $139,048 to $154,144. 
• 90% of all CEOs in the electronics industry have salaries that fall between $139,048 to $154,144
• We are 90% confident that the mean salary of the sampled CEOs falls in the interval $139,048 to $154,144.

A recent survey found that out of 400 random American adults, 89% pay their bills on time. The margin of error in this survey was 2%. What is the interval of values in which the truth is likely found?

• 89% - 91%

• 87% - 89%

• 87% - 91%

• 388 - 402

A research team surveys 200 high schoolers at glenoak. They find that 57% of them drive to school every day. What is the margin of error?

• 95%

• 14%

• 7%

• 3%

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. Interpret the confidence level.

• If the puzzle editor took many random samples of subscribers and constructed a 99% confidence interval for each sample, about 99% of these intervals would capture the true median completion time for all subscribers.

• If the puzzle editor took many random samples of subscribers and constructed a 99% confidence interval for each sample, about 99% of these intervals would not capture the true median completion time for all subscribers.

• If the puzzle editor took many random samples of subscribers and constructed a 90% confidence interval for each sample, about 90% of these intervals would capture the true median completion time for all subscribers.

• If the puzzle editor took many random samples of subscribers and constructed a 15.2% confidence interval for each sample, about 18.6% of these intervals would capture the true median completion time for all subscribers.

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. Interpret the confidence level.

• If the principal took many random samples of students and constructed a 90% confidence interval for each sample, about 90% of these intervals would capture the true mean number of hours doing homework per week for all students of the school.

• If the principal took many random samples of students and constructed a 90% confidence interval for each sample, about 90% of these intervals would not capture the true mean number of hours doing homework per week for all students of the school.

• If the principal took many random samples of students and constructed a 2,3% confidence interval for each sample, about 2.3% of these intervals would capture the true mean number of hours doing homework per week for all students of the school.

• If the principal took many random samples of students and constructed a 4.1% confidence interval for each sample, about 4.1% of these intervals would capture the true mean number of hours doing homework per week for all students of the school.