Mean Confidence Intervals

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.

A local bank needs information concerning the savings account balances of its customers. A random sample of 13 accounts was checked. The mean balance was $686.75 with a sample standard deviation of $256.20. Find a 95% confidence interval for the true mean.

• ($513.14, $860.36)

• ($525.59, $847.91) 

• ($533.27, $840.23)

• ($531.93, $841.57)

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 ,94.92)

• (87.269, 96.731)

• (87.29, 96.71)

• (87.77, 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. (Round to the nearest whole number)

• (1070, 2530)

• (1273, 2326)

• (1799, 1801)

• (1776, 1823)

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.

• .2

• μ

• 12

• n

• 2.40

• Z

• 1.96

• σ

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.

• 12.30 < μ < 7.82

• 7.82 < μ < 12.30

• 7.74 < μ < 12.46

• 12.40 < μ < 7.72

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)

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.

• 12

• μ

• 1.96

• Z

• 2.40

• n

• .2

• σ

A random sample of 100 visitors to a popular theme park spent an average of $142 on the trip with a standard deviation of $47.5. 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)

• ($132.77, $151.43)

• ($132.69, $151.31)

• ($140.88, $143.12)

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