3/1/01Coley / P. Myers / Wylder

AP Statistics

3/1/01Coley / P. Myers / Wylder

Test #10 (Chapter 10)Name ______

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

1. If the 90% confidence interval of the mean of a population is given by , which of the following is correct?

(a) There is a 90% probability that the true mean is in the interval.

(b) There is a 90% probability that the sample mean is in the interval.

(c) If 1,000 samples of the same size are taken from the population, then approximately 900 of them will contain the true mean.

(d) There is a 90% probability that a data value, chosen at random, will fall in the interval.

(e) None of the above.

2. Which of the following will reduce the width of a confidence interval?

1. Increasing the confidence level.
2. Increasing the sample size.
3. Decreasing the standard deviation.

(a) I only

(b) I and II only.

(c) II and III only.

(d) I, II, and III.

(e) None of the above.

3. Which of the following is true?

(a) A highly significant result indicates that the sample result never really happened.

(b) If the probability of sample data yielding a statistic as or more extreme than a given value is approximately 0, then we have a good indication that bias must have been involved with the data collection.

(c) If the probability of sample data yielding a statistic as or more extreme than a given value is approximately 0, then we have a good indication that the value of the parameter could be significantly different than what is stated.

(d) If the probability of sample data yielding a statistic as or more extreme than a given value is approximately 0, then we have a good indication that whoever stated the expected value is lying.

(e) None of the above.

4. The P-value of a test of significance is the probability that:

(a) The decision resulting from the test is correct.

(b) 95% of the confidence intervals will contain the parameter of interest.

(c) The null hypothesis is true.

(d) The alternative hypothesis is true.

(e) None of the above.

5. Given , which of the following is true?

(a)

(b) The power of the test is .95.

(c) = P (Rejecting H0 when H0 is true).

(d) = P (Rejecting H0 when H0 is false).

(e) The value of is independent of the value of .

6. Given: , if you conclude that the mean is less than 30 when it is actually 27:

(a) You have made a Type II error.

(b) You have made a Type I error.

(c) The result of your test was not significant.

(d) You have drawn a correct conclusion.

(e) All of the above are true.

7. What assumptions are necessary to validate a 95% confidence interval from a sample size 6 of the form: ?

1. The sample must have been randomly drawn from the population.
2. The population is approximately normal.
3. The population standard deviation must be known.

(a) I only.

(b) I and II only.

(c) I and III only.

(d) I, II, and III.

(e) None of the above.

8. In general, how does doubling the sample size change the confidence interval size?

(a) Doubles the interval size.

(b) Halves the interval size.

(c) Multiplies the interval size by .

(d) Divides the interval size by .

(e) Cannot be determined without knowing the sample size.

1. A coffee-dispensing machine is supposed to deliver 8 ounces of liquid into each paper cup, but a consumer believes that the actual amount is less. As a test he plans to obtain a sample of 36 cups of the dispensed liquid and, if the mean content is less than 7.75 ounces, to reject the 8-ounce claim. If the machine operates with a standard deviation of 0.9 ounces, what is the probability that the consumer will mistakenly reject the 8-ounce claim even though it is true?

(a) 0.0478

(b) 0.0950

(c) 0.1500

(d) 0.3897

(e) 0.4525

1. A pharmaceutical company executive claims that a medication will produce a desired effect for a mean time of 58.4 minutes. A government researcher runs a hypothesis test of 250 patients and calculates a mean of 59.5. If the population standard deviation is known to be 7.6, in the which of the following intervals is the P-value located?

(a) P < .01

(b) .01 < P <.025

(c) .025 < P < .05

(d) .05 < P < .10

(e) P > .10

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

1. A triathlon consisting of swimming, cycling, and running is one of the more strenuous amateur sporting events. A study was done on maximal heart rate of 9 randomly selected male triathletes. The results were:

1. Assuming that the heart-rate distribution for each event is approximately normal, construct 95% confidence intervals for the true mean heart rate of triathletes for each event.

b. Do the intervals in part a overlap? Based on the computed intervals, do you think there is evidence that the mean heart rate for running is higher than the other two events? Explain.

1. An association of college bookstores reported that the average amount of money spent by students on textbooks for the Fall 1999 semester was $325.16 with a standard deviation of $76.42. A random sample of 75 students at the local campus of the state university indicated an average bill for textbooks for the semester in question to be $312.34. Does the data indicate () that the actual average bill is different from the $325.16 that was reported? Give appropriate statistical evidence to support your conclusion.

1. A pharmaceutical manufacturer does a chemical analysis to check the potency of products. The standard release potency for cephalothin crystals is 910 () and the manufacturer believes this claim may be too high. An assay of 16 lots gives the following potency data:

1. Test the manufacturer’s claim at the 0.01 level of significance. Write your decision rule in terms of z.

b. If the true population mean is in fact 906, determine the power of the test. Explain clearly the meaning of your result.

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