Confidence Intervals for Means Sigma Known

The amount added and subtracted to the statistic.

• Margin of Error

• Point Estimator

• Statistic

• Population

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.

Which of the following values below represents the critical value for a 98% confidence interval?

• 2.326
• 2.054
• 1.645
• 3.091

The confidence level of an interval estimate of a parameter is the probability that the interval estimate will contain the parameter.

• True
• False

Find the value of z_c for a 90% confidence interval.

• -1.96 
• 1.645
• 1.440
• -1.598

Given the same mean, SD, and sample size, a confidence interval of 80% would be wider than a confidence interval of 90%

• True
• False

In a crash test of 15 troopers, collision repair costs are found to have a distribution that is approximately normal, with a mean of $1800 and a sample standard deviation of $950. Construct a 99% confidence interval for the repair cost. 

• (1069.77, 2530.23)
• (1077.13, 2522.87)
• (1167.15, 2432.85)
• None of these.

A sample of 40 people owned an average of 1.35 apple products. It is known from a previous study that the population standard deviation of apple product ownership is 0.63 products. Construct a 95% confidence interval.

• (1.11, 1.58)
• (1.15, 1.55)
• (1.19, 1.51)
• (1.09, 1.61)

A random sample of 100 visitors to a popular theme park spent an average of $142 on the trip with a sample standard deviation of $47.50. Which of the following would be the 98% confidence interval for the mean money spent by all visitors to this theme park?

• ($130.77, $153.23)
• ($130.96, $153.07)
• ($132.69, $151.31)
• ($140.88, $143.12)