AP Stats Lesson 7.1-7.2

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 quality control specialist at a glass factory must estimate the mean clarity rating for a new batch of glass using a sample of 18 glass sheets from the batch. Past investigations show that clarity ratings are normally distributed. The specialist decides to use a t-distribution rather than a z-distribution because ...

• The t distribution is more accurate than a z distribution.

• Clarity ratings for the entire bacth are normally distributed.

• The t-distribution will create a narrower interval than z.

• The standard deviation for the population is unknown.

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

Which of the following changes to a study would result in a narrower confidence interval?

• increasing the confidence level, increasing the sample size
• decreasing the confidence level, decreasing the sample size
• increasing the confidence level, decreasing the sample size
• decreasing the confidence level, increasing the sample size.

What are the critical t-values for an 80% confidence interval given a sample size of 16?

• $\pm1.341$

• $\pm1.337$

• $\pm1.753$

• $\pm1.746$

What are the critical t-values for an 95% confidence interval given a sample size of 4?

•  $\pm4.541$ 

•  $\pm3.747$ 

•  $\pm3.182$ 

•  $\pm2.776$ 

What are the critical t-values for an 98% confidence interval given a sample size of 4?

•  $\pm4.541$ 

•  $\pm3.747$ 

•  $\pm3.182$ 

•  $\pm2.776$ 

As the sample size (n) increases, the  $t$ -distribution starts to look more and more like the...

• Normal distribution

• Binomial distribution

• Poisson distribution

• Geometric distribution

 $df=$  

•  $n$  

•  $n-1$  

•  $\sqrt{n}$  

•  $\sqrt{n-1}$  

 Which of the following conditions must be met for it to be appropriate to use $s$ as a substitute for  $\sigma$ ? Check all that apply. 

•  $\sigma$ is unknown

•  $\mu$ is unknown

• The sample size is at least 30

• The data distribution is approximately normal