Interpreting Confidence Intervals

What can you do to reduce the margin of error? 

• increase the confidence level

• decrease the confidence level

• increase sample size

• decrease sample size

What critical value t* is used in constructing a 99% confidence interval based on n = 12 randomly selected observations. 

• 3.106

• 3.055

• 2.58

• 1.96

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.

• There is a 90% probability that all CEOs in the electronics industry have salaries that fall between $139,048 to $154,144.

• We are 95% confident that the mean salary of all CEOs in the electronics industry falls in the interval $139,048 to $154,144.

Suppose a SRS of 45 people who work in a city take an average os 21 minutes to get to work. We calculate a 95% confidence interval and get (18.3, 23.7).

Which of the following statement(s) is(are) an INACCURATE interpretation the confidence level?

• 95% of the 45 workers take between 18.3 and 23.7 minutes to get to work.

• There is a 95% chance that the mean time it takes all workers in this city to get to work is between 18.3 and 23.7 minutes.

• We are 95% confident that the mean time it takes all workers in the city to get to work is between 18.3 and 23.7 minutes.

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

• statistic

• parameter

Answer explanation

The confidence interval is all about capturing the true mean (parameter).

You use the sample data (statistic) to construct the confidence interval, but the interval is about the true mean.

Which z-value is used for a 95% confidence interval?

• 2.58

• 1.66

• 1.96

• 2.33

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

• 90%

• 95%

• 97%

• 99%

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?

• 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.

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.

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