Finding Confidence Intervals

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

Increasing the sample size __________ the confidence interval. 

• increases

• decreases

• does not affect

• there is not enough evidence to determine the answer

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)

In a survey of 104 students, it was found that 79 went to the homecoming game this year.

Calculate a 99% confidence interval for p.

• (.59, .79)

• (.62, .85)

• (.60, .90)

• (.65, .87)

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 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

The football coach randomly selected ten players and timed how long each player took to perform a certain drill. The times (in minutes) were: 13.2, 5.1, 7.5, 8.0, 12.7, 7.6, 13.8, 14.5, 7.7, and 10.5. Determine a 95 percent confidence interval for the mean time for all players.

• 12.42 < μ < 7.70

• 7.82 < μ < 12.30

• 7.70 < μ < 12.42

• 12.30 < μ < 7.82

An IQ test was given to a simple random sample of 75 students at a certain college. The sample mean score was 105.2. Scores on this test are known to have a standard deviation of 10. It is desired to construct a 90% confidence interval for the mean IQ scores of the students at the college. Find the point estimate.

• 10

• 105.2

• .90

• 75