Significance Tests Worksheet AP Statistics Name:___________________________
1. A fitness center advertises that the average pulse rate of its members is 68.4 bpm. A high school AP Statistics instructor suspects this is a made-up number and runs a hypothesis test on an SRS of 48 members, calculating a mean of
71.0 bpm with a standard deviation of 10.3 bpm. In which of the following intervals is the p-value located?
(a) p < .01
(b) .01 < p < .02
(c) .02 < p < .05
(d) .05 < p < .10
(e) p < .10
2. In a one-sided hypothesis test for the mean, for a random sample of size 15 the t -score of the sample mean is 2.615. Is this significant at the 5 percent level? At the 1 percent level?
(a) Significant at the 1 percent level but not at the 5 percent level
(b) Significant at the 5 percent level but not at the 1 percent level
(c) Significant at both the 1 percent and 5 percent levels
(d) Significant at neither the 1 percent nor 5 percent levels
(e) Cannot be determined from the given information
3. A quality inspector plans to test a sample of 40 bottles of soft drink labeled at 20 ounces. If she finds the mean content to be less than 19.8 ounces, she will have the bottling machinery stopped and recalibrated. If it is known that the machine operates with a standard deviation of 0.75 ounces, what is the probability that the inspector will mistakenly stop a machine that is delivering a mean of at least 20 ounces per bottle?
(a) .023
(b) .046
(c) .051
(d) .092
(e) .119
4. A researcher believes that a new diet should improve weight gain in laboratory mice. If the average gain for 12 mice on the new diet is 5.3 ounces with a standard deviation of 0.5 ounces, while 15 control mice on the old diet gain an average of 5 ounces with a standard deviation of 0.4 ounces, where is the p -value?
(a) Below .01
(b) Between .01 and .025
(c) Between .025 and .05
(d) Between .05 and .10
(e) Over .10
5. Which of the following are true statements?
I. The probability of a Type II error does not depend on the probability of a Type I error.
II. In conducting a hypothesis test, it is possible to simultaneously make both a Type I and Type II error.
III. A Type II error will result if one incorrectly assumes the data are normally distributed.
(a) I only
(b) II only
(c) III only
(d) I, II, and III
(e) None are true

6. An assembly line machine is supposed to turn out bowling balls with a diameter of 8.55 inches. Each day an SRS of five balls are pulled and measured. If their mean diameter is under 8.35 inches or over 8.75 inches, the machinery is stopped and an engineer is called to make adjustments before production is resumed. The quality control procedure may be viewed as a hypothesis test with 𝐻
0
: 𝜇 = 8.55
and 𝐻 𝑎
: 𝜇 ≠ 8.55
. What would a Type II error result in?
(a) A warranted halt in production to adjust the machinery
(b) An unnecessary stoppage of the production process
(c) Continued production of wrong size bowling balls
(d) Continued production of proper size bowling balls
(e) Continued production of bowling balls that randomly are the right or wrong size
7. First-year high school students were randomly put into either traditional math classes or math classes taught with a new innovative approach. In a standard algebra test, 230 traditionally taught students scored an average of 76.5 with a standard deviation of 7.4, while 185 students under the new approach averaged 78.8 with a standard deviation of 5.6. Is there sufficient evidence of a difference in the test results – what is the test statistic for 𝜇
2
≠ 0 ?
(a) 𝑡 =
76.5−78.8
√
(7.4)2
230
+
(5.6)2
185
(b) 𝑡 = 2
76.5−78.8
√
(7.4)2
230
+
(5.6)2
185
(c) 𝑡 =
76.5−78.8
(
7.4
√230
+
5.6
√185
)
𝐻
0
: 𝜇
1
− 𝜇
2
= 0 and 𝐻 𝑎
: 𝜇
1
−
(d) 𝑡 = 2
76.5−78.8
(
7.4
√230
+
5.6
√185
)
(e) 𝑡 =
76.5−78.8
(
6.5
√207.5
)
8. An SRS of 100 students at schools using an innovative math program scored an average of 357 with a standard deviation of 54 on a state test; an SRS of 150 students at schools using a traditional approach scored an average of 343 with a standard deviation of 62 on the same state test.
(a) Is there evidence that students using the innovative approach have a higher average score than students using the traditional approach? Give statistical justification for your answer.
(b) Assuming standard deviations of 54 and 62 as above, how large a sample (same number for both) should be used to be 95 percent sure of knowing the difference in scores to within 10.