Find the Confidence Intervals

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.

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

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 Critical Value for the mean.

• 1.67

• 1.28

• -1.67

• -1.28

What is the point estimate, p̂, of this sample?

• .322

• .342

• .465

• .511

What is the margin of error of this sample?

• .21

• .344

• .14

• .342

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

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