AP StatisticsName ______
3/1/07Coley / P. MyersPeriod ______
Test #10 (Chapter 23-25)Honor Pledge ______
Part I - Multiple Choice (Questions 1-10) - Circle the answer of your choice.
1. Two types of football helmets, padded helmets and suspension helmets, were compared to determine which had the lowest rate of impact damage. Forty helmets of each type were randomly selected and subjected to an impact test. The damage rates were 0.14 (padded) and 0.45 (suspension). A 95% confidence interval estimate for the difference in the damage rates of the two types of helmets is (-0.498, -0.122). On the basis of this confidence interval, can you say that the padded helmets have a significantly lower rate than suspension helmets?
(a) No, because confidence intervals cannot be used to test hypotheses.
(b) No, because rates cannot be negative.
(c) Yes, because (-0.122) – (-0.498) = 0.376 which is greater than zero.
(d) Yes, because clearly 0.14 is less than 0.45.
(e) Yes, because the entire confidence interval is negative.
2. The standard error of refers to
(a)the amount an observed statistic value for differs from its parameter.
(b)the standard deviation of the sampling distribution of .
(c)the number of standard deviations that the observed statistic value differs from its parameter .
(d)the maximum amount that the values of the statistic differ from the parameter value .
(e)the amount of variation in the data about the mean.
3. Data was collected to test whether there is a difference between the mean heights of women born in two different countries. It is assumed that the heights of women in each of these countries are approximately normally distributed. The data collected indicate the following:
Which of the following represents an estimate of the standard deviation of the sampling distribution corresponding to ?
(a)0.04
(b)0.29
(c)2.24
(d)2.50
(e)3.16
4. You want to compute a 90% confidence interval for the mean of a population with unknown population standard deviation. If the sample size is 30, what is the appropriate value of t*?
(a) 0.90
(b) 1.311
(c) 1.645
(d) 1.699
(e) 1.96
5. In a hypothesis test for the mean of a population, if 0.64 is the standard error of the mean and the sample size is 25, what is the standard deviation of the sample?
(a) 3.2
(b) 0.64
(c) 32
(d) 0.128
(e) none of the answers given are correct
6. If the P-value of the test is less than the level of significance of the test, then which of the following is a correct conclusion?
I. The value of the test statistic is in the rejection region for this test.
II. The sample size should be increased to decrease the margin of error.
III. The corresponding confidence interval will not contain the hypothesized value of the parameter in the null hypothesis.
(a) I only
(b) I and II only
(c) I, II, and III
(d) I and III only
(e) II and III only
7. A geologist claims that a particular rock formation will yield a mean amount of 24 pounds of a chemical per ton of excavation. His company, fearful that the true amount will be less, plans to run a test on a random sample of 50 tons. They will reject the 24 pound claim if the sample mean is less than 22. Suppose the standard deviation is 5.8 pounds. If the true mean is 20 pounds of chemical, what is the probability that the test will result in a failure to reject the incorrect 24 pound claim?
(a) 0.0073
(b) 0.4927
(c) 0.5073
(d) 0.8200
(e) 0.9927
8. A hypothesis test whose null hypothesis is is conducted at the level of significance. Which of the following statements is true?
(a) Since ,
(b) The power of the test is 0.98.
(c) The power of the test is 0.02.
(d) The power of the test cannot be calculated from this information.
(e) The value of , but the power of the test cannot be calculated from this information.
9. In a test of versus , a sample of size 220 leads to a p-value of 0.034. Which of the following must be true?
(a)A 95% confidence interval for calculated from these data will not include.
(b)At the 5% level if is rejected, the probability of a Type II error is 0.534.
(c)The 95% confidence interval for calculated from these data will be centered at .
(d)The null hypothesis will not be rejected at the 5% level.
(e)The sample size is insufficient to draw a conclusion with 95% confidence.
10. A pharmaceutical company claims that a medication will produce a desired effect for a mean time of 58.4 minutes. A government researcher runs a one-sided hypothesis test of 250 patients and calculates a mean of 57.5 with a standard deviation of 8.3. In which of the following intervals is the p-value located?
(a) p-value < .01
(b) .01 < p-value < .025
(c) .025 < p-value < .05
(d) .05 < p-value < .10
(e) p-value > .10
Part II – Free Response (Questions 11-12) – Show Your Work.
- The developers of a training program designed to improve manual dexterity claim that people who complete the 6-week program will increase their manual dexterity. A random sample of 12 people enrolled in the training program was selected. A measure of each person’s dexterity on a scale of 1 (lowest) to 9 (highest) was recorded just before the start of and just after the completion of the 6-week program. The data are shown in the table below.
Person / Before Program / After Program
A / 6.7 / 7.8
B / 5.4 / 5.9
C / 7.0 / 7.6
D / 6.6 / 6.6
E / 6.9 / 7.6
F / 7.2 / 7.7
G / 5.5 / 6.0
H / 7.1 / 7.0
I / 7.9 / 7.8
J / 5.9 / 6.4
K / 8.4 / 8.7
L / 6.5 / 6.5
Total / 81.1 / 85.6
Can one conclude that the manual dexterity for people who have completed the 6-week training program has significantly increased? Support your conclusion with appropriate statistical evidence.
- The principal at CrestMiddle School, which enrolls 500 sixth and seventh grade students, is interested in determining how much time students spend on homework each night. The table below shows the mean and standard deviation of the amount of time spent on homework each night (in minutes) for a random sample of 20 sixth-grade students and a separate sample of 20 seventh-grade students at this school.
Mean / Standard Deviation
Sixth-Grade Students / 27.3 / 10.8
Seventh-Grade Students / 47.0 / 12.4
Based on dotplots of these data, it is not unreasonable to assume that the distribution of times for each grade were approximately normally distributed.
(a)Estimate the difference in mean times spent on homework for all sixth- and seventh grade students in this school using a 95% confidence interval. Be sure to interpret this interval in the context of the problem.
(b) An assistant principal reasoned that a narrower confidence interval could be obtained if the students were paired based on their responses; for example, pairing the sixth-grade student and the seventh-grade student with the highest number of minutes spent on homework, the sixth-grade student and the seventh-grade student with the next highest number of minutes spent on homework, and so on. Is the assistant principal correct in thinking that matching students in this way and then computing a matched-pairs confidence interval for the mean difference in time spent on homework is a better procedure than the one used in part (a)? Explain why or why not.