Coley / P. Myers / Wylder

AP Statistics

Coley / P. Myers / Wylder

Hypothesis TestingName ______

Part I - Multiple Choice (Questions 1 – 11) - Circle the answer of your choice.

1. 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.

2. 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.

(d) The alternative hypothesis is true.

(e) None of the above.

3. Given , which of the following is true?

(a)

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

(d) P (Rejecting H0 when H0 is false) = .05.

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

4. 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.

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

(d)0.3897

(e)0.4525

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

7. Which of the following is a criterion for choosing a t-test rather than a z-test when making an inference about the mean of a population?

(a) The standard deviation of the population is unknown.

(b) The mean of the population is unknown.

(d) The population is not normally distributed.

(e) The sample size is less than 100.

8. What is the critical value t* which satisfies the condition that the t distribution with 8 degrees of freedom has probability 0.10 to the right of t*?

(a) 1.397

(b) 1.282

(d) 0.90

(e) cannot be determined

9. 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

10. A building inspector believes that the percentage of new construction with serious code violations may be even greater than the previously claimed 7%. She conducts a hypothesis test on 200 new homes and finds 23 with serious code violations. Is this strong evidence against the .07 claim?

(a) Yes, because the P-value is .0062

(b) Yes, because the P-value is 2.5

(b) No, because the P-value is only .0062

(d) No, because the P-value is over 2.0

(e) No, because the P-value is .045

11. Which of the following statements are statistically sound?

I. It is helpful to examine your data before deciding whether to use a one-sided or a two-sided hypothesis test.

II. If the P-value is .05, the probability that the null hypothesis is correct is .05.

III. The larger the P-value, the more evidence there is against the null hypothesis.

(a) I only

(b) II only

(d) II and III

(e) none of the above

Part II – Free Response (Questions 12-16) – Show your work and explain your results clearly.

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. 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 with a standard deviation of $76.42. 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.

A random sample of 415 potential voters was interviewed 3 weeks before the start of a state-wide campaign for governor; 223 of the 415 said they favored the new candidate over the incumbent. However, the new candidate made several unfortunate remarks one week before the election. Subsequently, a new random sample of 630 potential voters showed that 317 voters favored the new candidate.Do these data support the conclusion that there was a decrease in voter support for the new candidate after the unfortunate remarks were made? Give appropriate statistical evidence to support your answer.

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:

897 / 914 / 913 / 906 / 916 / 918 / 905 / 921
918 / 906 / 895 / 893 / 908 / 906 / 907 / 901

Test the manufacturer’s claim at the 0.01 level of significance.

b. If the true population mean is in fact 906, what type of error has been made? Is this a serious error?

15. A large university provides enough housing for 10 percent of its graduate students to live on campus. The university's housing office thinks that the percent of graduate students looking on campus may be more than 10 percent. The housing office decides to survey a random sample of graduate students, and 62 of the 481 respondents say that they are looking for housing on campus.

(a) On the basis of the survey data, would you recommend that the housing office consider increasing the amount of housing on campus available to graduate students? Give appropriate statistical evidence to support your recommendation.

(b) In addition to the 481 graduate students who responded to the survey, there were 19 who did not respond. If these 19 had responded, is it possible that your recommendation would have changed? Explain.

16. A manufacturer claims that its quality control is so effective that no more than 2% of the parts in each shipment are defective. As simple random sample of 100 parts from the last shipment contained 3 defectives.

(a) Why is a hypothesis test to determine the validity of the company's claim inappropriate? Explain your answer.

(b) What is the minimum sample size for which a test of the claim would be appropriate? Show your work.

(c) Suppose your answer in part (b) were the sample size. Perform an appropriate test of the manufacturer's claim at the 1% level of significance. Assume that the observed proportion is 0.03 for this sample size.