AP Statistics Sample T-Tests

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

To compare 2 dog-training programs, an obedience school trained 43 dogs using Program A and 41 dogs using Program B. For Program A, the average number of training hours required was 24.8 with a standard deviation of 3.1 hours. For Program B, the mean was 22.9 hours with a standard deviation of 3.3 hours. Is there a significant difference between the two programs?

• One-Sample Z Test for a Proportion

• One-Sample Z Test for a Mean

• Two-Sample T Test for the Difference in Means

• Two-Sample Z Test for the Difference in Means

The manager of a sporting goods store offered a bonus commission to his salespeople when they sold more goods. A new manager dropped the bonus system. For a random sample of six sales people, the weekly sales (in thousands of dollars) are shown in the following table with and without the bonus system
Salesperson   1 2 3 4 5 6
with bonus 2.9 3.0 5.8 4.4 5.3 5.6
w/o bonus 2.8 2.5 5.9 3.5 4.6 4.6
difference 0.1 0.5 -0.1 0.9 0.7 1.0

• Matched-Pairs T Test for a Mean

• One-Sample T Test for a Mean

• Two-Sample T Test for the Difference in Means

The following is based on information taken from Winter Wind Studies in Rocky Mountain National Park, by Glidden. At five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (mi/hr) in January and April are recorded below:
Weather station 1 2 3 4 5
January 139 122 126 64 78
April 104 113 100 88 61
Difference 35 9 26 -24 17
Does this information indicate that the peak wind gusts are higher in January than April?

• Two-Sample T Test for the Difference in

• Matched-Pairs T Test for a Mean

• One-Sample T Test for a Mean

What test should be performed?

• Paired t test

• 1 sample t test for mean difference

• 2 proportion z test

• 2 sample t test for difference in means

What test should be used?

• 2 Sample t test for difference in means

• 2 proportion z test

• Paired t test

• 1 sample z test

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.

What interval should be used?

• 2 Sample t interval for means

• Paired t interval

• Paired t test

• 1 proportion z interval

• The slope decreased and the r² increased.
• The slope increased and the r² decreased.
• The slope decreased but r² remained the same.
• Both slope and r² remained the same.