AP Stats Confidence Intervals 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)

A sample of 121 high school seniors were surveyed on their level of school spirit on a scale of 0-100. The sample mean of this survey is 86. The known population standard deviation is 14 for all seniors in the class. Which of these is a 95% confidence interval for the population mean?

• [82.7, 89.3]

• [83.5, 88.5]

• [83.9, 88.1]

• [85.9, 86.1]

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

• 7.72 < μ < 12.40

• 12.40 < μ < 7.72

A simple random sample of size 11 has a mean of 3.16. The population standard deviation is 1.75. The population is approximately normally distributed. Construct a 98% confidence interval for the population mean.

We are asked to find a confidence interval for the ​ (a)   .

σ is ​ (b)   .

The sample size is ​ (c)   , so it is not greater than 30.

The population is approximately normal. Hence, we should use the ​ (d)   method.

• known

• population mean

• z

• 11

• unknown

• 98%

• t

• sample mean

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

• Z

• 2.40

• σ

• .2

• n

• 1.96

• μ

• A

• B

• C

• D

• E