Confidence Intervals

Increasing the sample size __________ the confidence interval. 

• increases

• decreases

• does not affect

• there is not enough evidence to determine the answer

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

Suppose that $51,759 was the median income for all households in 2012. Does the interval ($51,484, $52,394) provide convincing evidence that the median household income increased in 2013? 

• Yes

• No

What can you do to reduce the margin of error? 

• increase the confidence level

• decrease the confidence level

• increase sample size

• decrease sample size

The lifetime of a certain type of batter is known to be normally distributed with a standard deviation of 20 hours. A sample of 50 batteries had a mean lifetime of 120.1 hours. Construct a 99% confidence interval for the mean lifetime of this type of battery.

• (111.2, 128.9)

• (114.53, 131.23)

• (112.52, 127.68)

• (118.43, 122.43)

Thirty randomly selected students took the calculus final. If the sample mean was 92 and the standard deviation was 9.4, construct a 99 percent confidence interval for the mean score of all students from which the sample was gathered.

• 87.27 < μ < 96.73

• 89.08 < μ < 94.92

• 87.29 < μ < 96.71

• 87.77 < μ < 96.23

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

• Standard deviation

• Sample size

• Critical value

• Sample mean

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

• decreasing the confidence level, increasing the sample size

• increasing the confidence level, decreasing the sample size

• increasing the confidence level, increasing the sample size

• decreasing the confidence level, decreasing the sample size