Confidence Intervals for Large Sample Means

Alexander computed roughly 1000 95%-confidence intervals in his life. How many of them contain the population mean?

• 1000

• roughly 950

• roughly 95

• roughly 50

Daniel and Tyron want to estimate the same population mean. Daniel collects a sample of 100 observations, Tyron of 200 observations. They both calculate 95% CI's.

• Daniels CI is roughly 2 times larger than Tyrons

• Daniels CI is roughly 1.5 times larger than Tyrons

• Daniels and Tyrons CI are roughly of the same size

• Daniels CI is two times smaller than Tyrons

A large standard deviation causes

• larger CI's

• smaller CI's

• Has no influence on CI's

• trouble calculating CI's

A large city newspaper periodically reports the mean cost of dinner for two people at restaurants in the city. The newspaper staff will collect data from a random sample of restaurants in the city and estimate the mean price using a 90 percent confidence interval. In past years, the standard deviation has always been very close to $35. Assuming that the population standard deviation is $35, which of the following is the minimum sample size needed to obtain a margin of error of no more than $5 ?

• 90

• 112

• 133

• 147

• 195

A random sample of 85 sixth-graders in a large city take a course designed to improve scores on a reading comprehension test. Based on this sample, a 90% confidence interval for the mean improvement μ in test scores for all sixth-graders in the city taking this course is found to be (12.6, 14.8). Which one of the following is a correct interpretation of this confidence interval?

• Ninety percent of the 85 sixth-graders in the sample improved their reading comprehension scores by 12.6 to 14.8 points.

• The probability is 0.90 that the true mean improvement in reading comprehension is between 12.6 and 14.8.

• We are 90% confident that the true improvement in reading comprehension scores is captured by the interval 12.6 to 14.8.

Suppose that a confidence interval for hours worked by students was computed to be (8.82, 10.78). Which of these is a valid interpretation of this confidence interval?

• There is a 95% probability that the average number of hours worked by all students is between 8.82 and 10.78 hours.

• There is a 95% probability that a randomly selected student worked between 8.82 and 10.78 hours.

• We are 95% confident that the population average number of hours worked by all students is between 8.82 and 10.78 hours.

• We are 95% confident that the average number of hours worked by the students in our sample is between 8.82 and 10.78 hours.

A 95% confidence level means...

• There is a 95% probability that the true population parameter falls within the interval.

• There is a 5% probability that the true population parameter falls within the interval.

• If we were to repeat the sampling process many times, 95% of the intervals constructed would contain the true population parameter.

2. A confidence level is:

• A. The probability that the true population parameter falls within the interval.

• B. The probability that the sample mean falls within the interval.

• C. The level of confidence we have that the interval contains the true population parameter.

• D. The margin of error for the estimate.

If a 90% confidence interval for the population mean is (10, 20), which of the following statements is true?

• There is a 90% probability that the true population mean falls within the interval.

• The sample mean is 15.

• If we were to repeat the sampling process many times, 90% of the intervals constructed would contain the true population mean.

• Both B and C.

Increasing the sample size will:

• A. Increase the width of the confidence interval.

• B. Decrease the width of the confidence interval.

• C. Have no effect on the width of the confidence interval.

• D. Increase the level of confidence.