Confidence Intervals

A sample of 30 women finds the mean height to be 62.3 in and the standard deviation to be 1.5 in. Find the margin of error of women's heights with a 95% CL.

• 699

• 0.56

• 0.537

• 19.325

In a crash test of 15 troopers, collision repair costs are found to have a distribution that is approximately normal, with a mean of $1800 and a standard deviation of $950. Construct a 99% confidence interval for the repair cost. 

• (1070, 2530)

• (1273, 2326)

• (1799, 1801)

• None of these.

Thirty randomly selected students took the calculus final. If the sample mean was 92 and the standard deviation was 9.4, construct a 99 percent confidence interval for the mean score of all students.

• 89.08 < μ < 94.92 

• 87.27 < μ < 96.73

• 87.29 < μ < 96.71 

• 87.77 < μ < 96.23

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 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.

A researcher constructs a 99% confidence interval for a population proportion and obtains an interval of (0.45, 0.55). Which of the following statements is true?

• There is a 99% probability that the true population proportion falls within the interval.

• The sample proportion is 0.50.

• If we were to repeat the sampling process many times, 99% of the intervals constructed would contain the true population proportion.

• 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.

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.