Interpreting Confidence Intervals

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.

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.

If a 99% confidence interval for a population mean is (100, 200) and a 95% confidence interval for the same population mean is (120, 180), 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 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.

A 95% confidence interval for a population mean is calculated as 45 ± 2. What is the sample mean?

• 43

• 45

• 47

• 44

Percentiles of the bootstrap distribution are provided. Use the percentiles to report a 95% confidence interval for the parameter.

• 6.593 hours to 7.78 hours

• 6.322 hours to 8.082 hours

• 6.438 hours to 7.947 hours

• 6.174 hours to 8.304 hours

Identify the confidence interval used in the figure below if each shaded area is equal to 0.05.

• 90%

• 95%

• 98%

• 99%

A confidence interval for the mean score of a test is (75, 85). What is the margin of error?

• 5

• 10

• 15

• 20