Test #8 (Chapter 22-23)Honor Pledge ______

AP StatisticsName ______

3/2/06Coley / P. MyersPeriod ______

Test #8 (Chapter 22-23)Honor Pledge ______

Part I - Multiple Choice (Questions 1-10) - Circle the answer of your choice.

1. In a test for acid rain, an SRS of 49 water samples showed a mean pH level of 4.4 with a standard deviation of 0.35. Find a 90% confidence interval estimate for the mean pH level.

(a) 4.4 0.01

(b) 4.40.08

(d) 4.40.35

(e) 4.40.58

2. The process of producing pain-reliever tablets with varying amounts of the active ingredient. It is claimed that the average amount of active ingredient per tablet is at least 200 milligrams. The Consumer Watchdog Bureau tests a random sample of 70 tablets. The mean content of the active ingredient for this sample is 194.3 milligrams with a standard deviation of 21 milligrams. What is the approximate p-value for the appropriate test?

(a) 0.012

(b) 0.024

(d) 0.100

(e) 0.488

3. The number of accidents per day at a large factory is noted for each of 64 days with a mean of 3.58 and a standard deviation of 1.52. With what degree of confidence can we assert that the mean number of accidents per day at the factory is between 3.20 and 3.96?

(a)48%

(b)63%

(d)95%

(e)99%

4. A weight loss clinic claims an average weight loss over 3 months of at least 15 pounds. A random sample of 50 of the clinic’s patrons shows a mean weight loss of 14 pounds with a standard deviation of 2.8 pounds. Assuming the distribution of weight losses is approximately normally distributed, what is the appropriate test for this situation, the value of the test statistics, and the associated P-value.

(a)z test; z=-2.53;P=.0057

(b)t test; t=-2.53; .01<P<.02

(c)z test; z=2.53; P=.0057

(d)t test; t=2.53; .005<P<.01

(e)z test; z=2.53; P=.9943

5. A 99% confidence interval for the weights of high school wrestlers is given as {125, 160}. Which of the following statements about this interval is true?

(a) At least 99% of the weights of high school wrestlers are in the interval {125, 160}.

(b) The probability is 0.99 that the true mean weight of high school wrestlers is in the interval {125, 160}.

(d) The procedure used to generate this confidence interval will capture the true mean weight of high school wrestlers 99% of the time.

(e) The probability is 0.99 that a randomly selected wrestler will weigh between 125 and 160 pounds.

6. Which of the following is true about the t distribution?

I. Its mean, median, and mode are all equal.

II. The t distribution is more spread out than the z distribution.

III. The greater the number of degrees of freedom, the greater the variance of the t distribution.

(a) I only

(b) II only

(d) I and II

(e) I and III

7. Two random samples of American adults are taken and the religious affiliations of the individuals involved are recorded. In the first sample of 200 adults, 66 of the individuals are Christians. In the second sample of140 adults, 11 of the individuals are Buddhists. Assume the two samples are independent. Which of the following should be used to construct a 95% confidence interval for the difference in proportions for adult Americans who practice the two religions?

(a)

(b)

(c)

(d) The conditions for constructing a confidence interval have not been met; therefore, a confidence interval should not have been computed.

(e) Because the sample sizes for the two proportions are not equal, a confidence interval cannot be computed.

8. A manufacturer constructs a 95% confidence interval for the average weight of the items he manufactures. His results need to be included in a report to his superiors, and the resulting interval is wider than he would like. In order to decrease the size of the interval the most, the manufacturer should take a new sample and

(a) increase the confidence level and increase the sample size.

(b) decrease the confidence level and increase the sample size.

(d) decrease the confidence level and decrease the sample size.

(e) The manufacturer will not be able to decrease the size of the interval.

9. Which of the following is not a characteristic for t-distributions?

(a) The t-distributions are mound-shaped.

(b) The t-distributions are centered at 0.

(d) The t-distributions use s as an estimate of .

(e) As the number of degrees of freedom decreases, the t-distribution approaches the normal distribution.

10. The condition np>10 and n(1-p)>10 for inference involving population proportions is important to guarantee

(a) random samples were taken

(b) the underlying binomial distribution is approximately normal

(d) unbiased estimation

(e) the sample data is accurate

Part II – Free Response (Questions 11-12) – Show your work and explain your results clearly.

11. An avid reader, Booker Worm, bets his friend, Wormer Book, that he reads books that average more than 375 pages in length. A random sample of 13 books on his shelf had the following number of pages: 595, 353, 434, 382, 420, 225, 408, 422, 315, 502, 503, 384, and 420.

(a) Does the data support Booker winning the bet? (Test at the 0.05 level of significance.)

(b) Based on your conclusion to part (a), what do you know about the corresponding confidence interval?

12. A nutritionist wants to confirm her suspicion that women tend to prefer chocolate for dessert more often than men. She decides that it will be convenient to collect data on customers of a large and popular restaurant owned by her family. The restaurant has a practice of showing the daily selection of desserts on a tray to the customers. For 500 customers selected randomly over a one week period, the nutritionist notes the gender of the customer and the choice of dessert. The data is summarized in the table below.

Gender
Male / Female
Dessert / with Chocolate / 140 / 150
without Chocolate / 160 / 50

Test the nutritionist’s suspicion. ()