Confidence Intervals and Sample Size

What is the margin of error for the interval (6.8, 12.9)?

• 9.85

• 3.05

• 3.50

• 6.8

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

• increasing the confidence level, increasing the sample size
• decreasing the confidence level, decreasing the sample size
• increasing the confidence level, decreasing the sample size
• decreasing the confidence level, increasing the sample size.

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.

The 99% confidence interval for a proportion is (0.54, 0.72). What is p̂?

• 0.63

• 0.18

• 0.09

• 0.66

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

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 in test scores for all sixth-graders in the city taking this course is found to be (12.6, 14.8). Which of the following are the sample mean and margin of error on which this interval is based?

• Sample Mean = 13.7; Margin of Error = 1.1
• Sample mean = 13.7; Margin of Error = 2.2
• Sample mean is unknown; Margin of Error = 2.2

Which of the following does NOT have an affect on the width of a confidence interval?

• Sample mean
• Confidence Level
• Sample standard deviation
• Sample size

When interpreting the confidence interval, make sure that you are describing the

• statistic

• parameter

Agricultural researchers plant 100 plots with a new variety of corn and measure the mean yield for these plots in bushels per acre. They treat the 100 plots as a simple random sample of possible plots of corn (as researchers often do) and report a 95% confidence interval for the mean corn yield of (128.4, 131.6) bushels per acre. Which of the following is a correct interpretation of the 95% confidence level (notice it's asking for level not interval!)?

• We are 95% confident that the true mean yield for this new variety of corn is captured by the interval (128.4, 131.6) bushels per acre
• If many intervals were constructed this way from many independent sets of 100 plots, 95% of the intervals would capture the true mean corn yield.
• If many intervals were constructed this way from many independent sets of 100 plots, 95% of the time the true mean corn yield would be in the interval (128.4, 131.6) bushels per acre.

Which of the following sources of error is included in the margin of error

• chance variation in choosing a random sample.
• undercoverage.
• some of the subjects did not understand the questions.
• voluntary response.