AP Statistics Hypothesis Tests for Means

To test a claim about a mean, when the population standard deviation is unknown we use:

• z procedures

• Pythagorean Theorem

• t procedures

• np > 10 and n(1-p) > 10

Mrs. Trahan claims that her students' average score on the AP exam is 3.9. A random sample of 50 of her students' scores produce a mean score of 3.1 with a standard deviation of 1.5. Does this sample show evidence that Mrs. Trahan is overstating her average score?

• With a test statistic of -3.8 which is unlikely, it seems that Mrs. Trahan may be overstating her average AP score.

• With a test statistic of -4.7 which is unlikely, it seems that Mrs. Trahan may be overstating her average AP score.

• With a test statistic of -0.53 which is not unusual and this sample does not show evidence that Mrs. Trahan is overstating her average AP score.

You have an SRS of 23 observations from large population. The distribution of sample values is roughly symmetric with no outliers. What critical value would you use to obtain a 98% confidence interval for the mean of the population?

• 2.177

• 2.183

• 2.326

• 2.500

• 2.508

A quality control inspector will measure the salt content (in milligrams) in a random sample of bags of potato chips from an hour of production. Which of the following would result in the smallest margin of error in estimating the mean salt content σ ?

• 90% confidence; n = 25 

• 90% confidence; n = 50 

• 95% confidence; n =25 

• 95% confidence; n =50 

• n=100 at any confidence level 

A random sample of 100 pairs of ladies’ shoes had a mean size of 8.3. Assume the population standard deviation is 1.5.  Can you conclude that the mean size of ladies’ shoes differs from 8?  Use the 0.01 level of significance.

• 1.5

• x̄

• 8.3

• s

• 100

• σ

• N/A

• µ

• 8

• n

• A
• B
• C
• D

A random sample of 100 pairs of ladies’ shoes had a mean size of 8.3. Assume the population standard deviation is 1.5.  Can you conclude that the mean size of ladies’ shoes differs from 8?  Use the 0.01 level of significance. p-value is ​ (a)   ​ (b)   0.01 hence ​ (c)   the null hypothesis. ​ (d)   evidence to conclude that the mean size of ladies' shoes differs from 8.

• There is not enough

• 0.0482

• >

• we fail to reject

• We reject

• <

• There is enough

• 0.485

The U.S. Census Bureau reported that the mean area of U.S. homes built in 2009 was 2,438 square feet.  Assume that a simple random sample of 20 homes built in 2010 had a mean area of 2,514 square feet, with a standard deviation of 225 square feet.  Can you conclude that the mean area of homes built in 2010 is greater than that of homes built in 2009?  Use 0.01 level of significance. The p-value is ​ > ​ ; thus, ​ the null hypothesis. ​ evidence to conclude that the mean area of homes built in 2010 is greater than that of homes built in 2009.

• 0.0737

• 0.0654

• we fail to reject

• we reject

• There is not enough

• There is enough

• 0.01

• 0.05

• A) Ho: The mean number of days 9th grade students absent is equal to the mean number of days 12th grade students are absent.
  Ha: The mean number of days 9th grade students absent is less than the mean number of days 12th grade students are absent.
• B) Ho: The mean number of days 12th grade students absent is less than the mean number of days 9th grade students are absent.
  Ha: The mean number of days 12th grade students absent is equal to the mean number of days 9th grade students are absent.
• C) Ho: The mean number of days 12th grade students absent is equal to the mean number of days 9th grade students are absent.
  Ha: The mean number of days 9th grade students absent is greater than the mean number of days 12th grade students are absent. 
• D) Ho: The mean number of days 12th grade students absent is equal to the mean number of days 9th grade students are absent.
  Ha: The mean number of days 12th grade students absent is less than the mean number of days 9th grade students are absent.

What interval should be used?

• 2 Sample t interval for means

• Paired t interval

• Paired t test

• 1 proportion z interval