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PRACTICE Name: TEST 3
1. Children in the same family exhibit a very strong tendency to have similar heights at similar ages. Hence, a plausible value for the correlation between heights of two children of the same parents, at similar ages, is a) r = 0.93 b) r = 0.15 c) r = 0.00 d) r = -0.15 e) r = -0.93. 2. The correlation between average monthly temperature x and monthly natural gas consumption y over a period of months at Lincoln High School is r = 0.86. Which of the following operations could change the value of the correlation? a) We measure gas consumption in cubic meters instead of cubic feet. b) We remove two outliers from the data before doing the calculation. c) We measure temperature in degrees Kelvin instead of in degrees Fahrenheit. d) All of the above. 3. If a hypothesis test gives a P-value of 0.30, a) the margin of error is 0.30. b) we have good evidence against the null hypothesis. c) the null hypothesis is very likely to be true. d) we do not have good evidence against the null hypothesis. 4. Which of the following P-values is statistically significant at the 1% level? a) P-value = .032 b) P-value = .002 c) P-value = .999 d) P-value = 0.10 5. A study claims that the mean IQ of statistics teachers is at least 130. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis? a) There is not sufficient evidence to support the claim 130. b) There is not sufficient evidence to reject the claim 130. c) There is sufficient evidence to reject the claim 130. d) There is sufficient evidence to support the claim 130. 6. The national unemployment rate last month was 4.3%. You think the rate may be different in your city, so you plan a sample survey that will ask the same questions as the Current Population Survey. In terms of p, what are your null and alternative hypotheses? a) H0: p = 0.43 and HA : p 0.43 b) H0: p = 0.043 and HA : p < 0.043 c) H0: p = 0.043 and HA : p 0.043 d) H0: p = 0.043 and HA : p > 0.043 7. Find the critical values for a sample with n = 10 and = 0.05 if H0: 20. a) -1.833 b) -2.262 c) -3.250 d) -1.383 8. The null hypothesis is a) another name for the alternative hypothesis. b) true with 95% probability. c) usually a statement of "no effect" or "no difference". d) statistically significant. 9. Suppose you want to test the claim that 3.5. Given a sample size of n = 31 and a level of significance of
= 0.10 when should you reject H0 ? a) Reject H0 if the standardized test statistic is greater than 1.96 or less than - 1.96 b) Reject H0 if the standardized test statistic is greater than 1.645 or less than - 1.645. c) Reject H0 if the standardized test statistic is greater than 2.575 or less than - 2.575. d) Reject H0 if the standardized test statistic is greater than 2.33 or less than - 2.33 10. If we are testing the null hypothesis H0: = 7 versus HA: > 7 and we compute our test statistic to be z = 2.5 (i.e. the standard score is 2.5), then: a) we have convincing evidence that is greater than 7. b) we fail to have convincing evidence that is greater than 7. c) we have "significant" results, with a p-value that is less than 0.05. d) we fail to have "significant" results, with a p-value that is greater than 0.05. e) both (a) and (c) f) both (b) and (d) 11. If we reject the null hypothesis when, in fact, it is true, we have a) made a correct decision. b) made a Type I error. c) made a Type II error. 12. Suppose we want to determine if the average height of all adult American males between the ages of 18 and 21 is now over 6 feet. What hypotheses should we use? a) H0: = 6 and HA : < 6 b) H0: p = 6 and HA : p > 6 c) H0: = 6 and HA : 6 d) H0: = 6 and HA : >6 13. Suppose you are using = 0.01 to test the claim that = 1120 using a P-value. are You given the sample statistics n = 35, x = 1090, and s = 82. Find the P-value. a) 0.0308 b) 0.0077 c) 0.0154 d) 0.3169 14. A university administrator obtains a sample of the academic records of past and present scholarship athletes at the university. The administrator reports that no significant difference was found in the mean GPA for male and female scholarship athletes (P-value = 0.287). This means a) the GPAs for male and female scholarship athletes are identical except for 28.7% of the athletes. b) the chance that a pair of randomly chosen male and female scholarship athletes would have a significant difference in GPAs is 0.287. c) the chance of obtaining a difference in the GPAs between male and female scholarship athletes like the one observed in the sample (or more extreme) if there is really no difference in the mean GPAs is 0.287. d) the maximum difference in GPAs between male and female scholarship athletes is 0.287. 15. A brewery claims that the mean amount of beer in their bottles is at least 12 ounces. Determine whether the hypothesis test for this claim is left-tailed, right-tailed, or two-tailed. a) left-tailed b) right-tailed c) two-tailed 16. A Type II error consists of a) rejecting the null hypothesis when it is true. b) rejecting the null hypothesis when it is false. c) failing to reject the null hypothesis when it is false. d) failing to reject the null hypothesis when it is true.
17. The Chicago Tribune claims that the mean age of bus drivers in Chicago is 47.4 years. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis? a) There is sufficient evidence to reject the claim = 47.4. b) There is not sufficient evidence to support the claim = 47.4. c) There is sufficient evidence to support the claim = 47.4. d) There is not sufficient evidence to reject the claim = 47.4. Remember, you must show all of your work to receive full credit for short answer questions on the test. 18. A fast food outlet claims that the mean waiting time in line is less than 4.9 minutes. A random sample of 60 customers has a mean of 4.8 minutes with a standard deviation of 0.6 minute. If = 0.05, test the fast food outlet's claim. 19. An SRS of 100 laborers who use the services of a national temporary employment agency found that in the past year the average number of days worked by these laborers was x =107 days. The standard deviation of these workers is s = 45 days. Carry out the appropriate test of significance, using = .05, to determine if the mean is different from the value of 120 days from 5 years ago. Be sure to show ALL the steps of this hypothesis test. 20. Clearly explain the meaning of the P-value you found in question 19. 21. The Metropolitan Bus Company claims that the mean waiting time for a bus during rush hour is less than 7 minutes. A random sample of 20 waiting times has a mean of 5.2 minutes with a standard deviation of 2.1 minutes. At = 0.01, test the bus company's claim using critical values. Assume the distribution is normally distributed. 22. Fifty-five percent of registered voters in a congressional district are registered Democrats. The Republican candidate takes a poll to assess his chances in a two-candidate race. He polls 1200 potential voters and finds that 621 plan to vote for the Democratic candidate. Test the claim that the Republican candidate will lose (i.e. the Republican candidate will receive less than half of the votes.). Use = 0.05. 23. An experiment is carried out to determine whether a new anesthetic results in lower death rates than other anesthetics. (Be your answers are specific to this particular situation!) a) What should the null hypothesis be? b) What should the alternative hypothesis be? c) Describe a possible Type I error for this situation. d) Describe a possible Type II error for this situation.