Interpreting Confidence Intervals

1. A 95% confidence level means...

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

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

• C. 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.

3. 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 mean of the sample is 15

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

4. 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?

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

• B. The sample proportion is 0.50.

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

• D. Both B and C.

5. 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.

True or False: The more confident you want to be, the smaller your confidence interval will be.

• True

• False

Which of the following changes to a study would result in a smaller confidence interval?

• increasing the confidence level, increasing the sample size

• increasing the confidence level, decreasing the sample size

• decreasing the confidence level, decreasing the sample size

• decreasing the confidence level, increasing the sample size.

What is the format for interpreting a confidence interval? 

• The interval from ___ to ___ captures the true mean in context.
• C% of samples of the same size taken from the same population will capture the parameter in question
• There is convincing evidence that C% gives the interval (___, ___) capturing the parameter in question.
• We are C% confident that the interval from ___ to ___ captures the [parameter in context].

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.

Complete the equation: 
point estimate +/- _____

• standard deviation
• margin of error
• critical value
• confidence level