AP Statistic Confidence Interval for Means

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 to $154,144. Give the 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% chance that 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.

Complete the equation: 
point estimate +/- _____

• standard deviation

• margin of error

• critical value

• confidence level

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].

What is the critical value z* for a 99% confidence interval? 

• -2.58

• 1.96

• -1.64

• 2.58

Given the interval (1.2, 1.8), what is the point estimate and the margin of error? 

• 1.5, 0.6

• 1.5, 0.3

• 1.2, 0.3

• 1.2, 0.6

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

Find the critical value, z*, for 91% confidence.

• 70

• 34

• 0.18

• -34

Find the critical value, z* for 97%

• 1.88

• 2.17

• -1.88

• -2.17

Which confidence would result in a wider interval (assuming nothing else changed), 91% or 97%?

• 97%, z* is larger for higher confidence intervals

• 97%, the standard error is larger for higher confidence intervals

• 91%, z* is larger for lower confidence intervals

• 91%, the standard error is smaller for lower confidence intervals

What is the margin of error of this sample?

• 0.28

• 0.14

• 0.342

• 0.684