Confidence Interval for Means

A sample of 20 cupcakes found the interval for average calories to be (150, 350). Which is the correct interpretation of the 95% confidence interval?

• We are 95% confident that the true mean caloric content can be found with a sample of 150 to 350 cupcakes.

• We are 95% confident that the interval (150, 350) captures the true average caloric content.

• We are 95% confident that a sample of 20 cupcakes will find 250 calories per cupcake.

• None of these are correct.

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.

• 89.08 < μ < 94.92

• 87.27 < μ < 96.73

• 87.29 < μ < 96.71

• 87.77 < μ < 96.23

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 standard deviation of $950. Construct a 99% confidence interval for the repair cost for the population.

• (1070, 2530)

• (1273, 2326)

• (1799, 1801)

• (1776, 1823)

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. It is desired to construct a 99% confidence interval for the mean lifetime of this type of battery. What is the Confidence Interval to one decimal place?

• (114.5, 125.6)

• (112.8, 127.4)

• (112.82, 127.38)

• (114.56, 125.64)

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

• (89.08, 94.92)

• (87.27, 96.73)

• (87.29, 96.71)

• (87.77, 96.23)

You sample 12 bugs and find the sample mean is 2.40 cm. You are told the standard deviation is 0.2 cm. Find a 95% Confidence Interval.

Identify the Variables

• 1.96

• μ

• .2

• Z

• 2.40

• n

• 12

• σ

You sample 12 bugs and find the sample mean is 2.40 cm. You are told the standard deviation is 0.2 cm. Find a 95% Confidence Interval.

• 1.96

• n

• 12

• μ

• .2

• Z

• 2.40

• σ

We measure the height of 40 randomly selected women, in which the mean height is 175cm. We also know the population standard deviation is 20cm. Which of the following represents a 95% Confidence Interval?

• 175cm ±1.645* 3.16

• 175cm ± 1.96*3.16

• 175cm ± 1.96*20

• 175cm ± 1.645*40

You sample 16 students in your school, and they average 13 hours of TV a week. Assume the standard deviation is 3. Find a 99% Confidence Interval.

• 99% confident the population mean is between 11.77 and 14. 23

• 99% confident the population mean is between 11.53 and 14.47

• 99% confident the sample mean is between 11.06 and 14.96

• 99% confident the population mean is between 11.06 and 14.96

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)

• 
  ($132.69, $151.31)

• 
  

  ($130.96, $153.07)

• 
  ($140.88, $143.12)