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.

Tags

CCSS.HSS.IC.B.4

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.

Tags

CCSS.HSS.IC.B.4

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

Tags

CCSS.HSS.IC.B.4

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.

Tags

CCSS.HSS.IC.B.4

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?

•  $\pm4.541$ 

•  $\pm3.747$ 

•  $\pm3.182$ 

•  $\pm2.776$ 

Tags

CCSS.HSS.ID.A.4

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

•  $\pm4.541$ 

•  $\pm3.747$ 

•  $\pm3.182$ 

•  $\pm2.776$ 

Tags

CCSS.HSS.ID.A.4

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

Tags

CCSS.HSS.ID.A.4

 $df=$  

•  $n$  

•  $n-1$  

•  $\sqrt{n}$  

•  $\sqrt{n-1}$  

 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

Tags

CCSS.HSS.IC.B.4