Confidence Intervals 3

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.

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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.

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

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

• B. The sample mean is 15.

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

• D. Both B and C.

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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.

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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.

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].

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A 90% confidence interval for a population mean is determined to be 800 to 900. If the confidence is increased to 95% confidence while the sample statistics and sample size remain the same, the confidence interval

• becomes wider
• becomes narrower
• does not change

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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.

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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.

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Is this a correct interpretation of a confidence interval?

If the same population is sampled on numerous occasions and interval estimates are made on each occasion, the resulting intervals would bracket the true population parameter in approximately 95 % of the cases.

• Yes

• No

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