The distribution of SAT Math scores of students taking

1. The distribution of SAT Math scores of students taking • Calculus I at UTSA is skewed left with a mean of 625 and a standard deviation of 44.5. If random samples of 100 students are repeatedly taken, which statement best describes the sampling distribution of sample means? • A) Shape is normal with a mean of 625 and standard deviation of 44.5. • Shape unknown with a mean of 625 and standard deviation of 44.5. • Shape unknown with a mean of 625 and standard deviation of 4.45. • E) No conclusion can be drawn since the population is not normally distributed. B) Shape is normal with a mean of 625 and standard deviation of 4.45.

2. 2) A population has a normal distribution with a mean of 50 and a standard deviation of 10. If a random sample of size 9 is taken from the population, then what is the probability that this sample mean will be between 48 and 54? A)0.000 B) 0.228 C) 0.385 D) 0.399 E) 0.611

3. 3) Owners of a day-care chain wish to determine the proportion of families in need of day care for the town of Sugar Land. The owners of the day-care chain randomly sample 50 families in Sugar Land and find only 4% of the returned questionnaires indicate these families having a need for child day-care services. The 4% is best described as • the sample proportion of families in Sugar Land needing child day-care services. • B) the sample proportion of families in Sugar land with children needing day-care services. • C) the population proportion of families in Sugar Land with children needing day-care services. • D) the 30 families in Sugar Land needing day-care services for their children. • E) the 600 families in Sugar Land with children needing day-care services.

4. 4) In a hypothesis test, the decision between a one-sided and two-sided alternative hypothesis is based on: • Which one gives you a significant • result. • C) How accurate you wish the results of • the test. • D) The level of significance of the test. • E) The statement of the null hypothesis. B) The alternative hypothesis appropriate for the context of the problem.

5. 5) 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. C) 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

6. 6) A survey is to be taken to estimate the proportion of people who support the NATO decision to be actively involved in the Balkins (assume sample proportion is 0.50). Among the following proposed sample sizes, which is the smallest that will still guarantee a margin of error of at most 0.03 for a 95% confidence level? • 35 B) 70 C) 800 • E) 4300 D) 1100

7. 7) A manufacturer constructs a 95% confidence interval for the proportion of successfully completed products off the assembly line. His results need to be included in a report to his supervisors, and the resulting interval is wider that he would like. In order to decrease the size of the interval the MOST, the manufacturer should take a new sample and • increase the confidence level and increase the sample size. • c) increase the confidence level and decrease 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. b) decrease the confidence level and increase the sample size.

8. 8) A survey of 300 union members in New York State reveals that 112 favor the Republican candidate for governor. Construct a 98% confidence interval for the percentage of all New York State union members who favor the Republican candidate. A) (31.9%, 42.8%) B) (30.1%, 44.5%) C) (26.7%, 47.9%) D) (26.7%, 47.9%) E) (30.8%, 43.8%)

9. 9) A state university wants to increase its retention rate of 4% for graduating students from the previous year. After implementing several new programs during the last two years, the university reevaluates its retention rate and comes up with a P-value of 0.075. What is reasonable to conclude about the new programs using α = 0.06? A) We can say there is a 7.5% chance of seeing the new programs having an effect on retention in the results we observed from natural sampling variation. We conclude the new programs are more effective. B) There's only a 7.5% chance of seeing the new programs having no effect on retention in the results we observed from natural sampling variation. We conclude the new programs are more effective. C) There is a 92.5% chance of the new programs having no effect on retention. D) We can say there is a 7.5% chance of seeing the new programs having no effect on retention in the results we observed from natural sampling variation. There is no evidence the new programs are more effective, but we cannot conclude the new programs have no effect on retention. E) There is a 7.5% chance of the new programs having no effect on retention.

10. 10) To plan the course offerings for the next year a university department dean needs to estimate what impact the "No Child Left Behind" legislation might have on the teacher credentialing program. Historically, 40% of this university's pre-service teachers have qualified for paid internship positions each year. The Dean of Education looks at a random sample of internship applications to see what proportion indicate the applicant has achieved the content-mastery that is required for the internship. Based on these data he creates a 90% confidence interval of (33%, 41%). Could this confidence interval be used to test the hypothesis p = 0.40 versus p < 0.40 at the α = 0.05 level of significance? A) No, because the dean only reviewed a sample of the applicants instead of all of them. B) Yes, since 40% is in the confidence interval he fails to reject the null hypothesis, concluding that there is not strong enough evidence of any change in the percent of qualified applicants. C) No, because he should have used a 95% confidence interval. D) Yes, since 40% is in the confidence interval he accepts the null hypothesis, concluding that the percentage of applicants qualified for paid internship positions will stay the same. E) Yes, since 40% is not the center of the confidence interval he rejects the null hypothesis, concluding that the percentage of qualified applicants will decrease.

11. 11) M&M Corporation advertises that 20% of the M&Ms produced will be orange in color. However, when our class experimented with these delightful treats we found the percentage of orange to be 18.9%. The value 18.9% is a ______, and the value 20% is a _____. A. parameter, statistic • parameter, parameter D. statistic, statistic B. statistic, parameter

12. 12) The distribution of values taken by a statistic in all possible samples of the same size from the same population is the A) probability that the statistic is obtained. B) population parameter. C) variance of the values. D) sampling distribution of the statistic. E) same shape as the population distribution.

13. 13) A factory produces plate glass with a mean thickness of 4 mm and a standard deviation of 1.1 mm. A simple random sample of 100 sheets of glass is to be measured, and the sample mean thickness of the 100 sheets is to be computed. The probability that the average thickness of the 100 sheets of glass is less than 4.1 mm is • 0.8183 • 0.5361 • 0.1817 • 0.6817 • 0.8413

14. 14) One month the actual unemployment rate in France was 13.4% If during that month you took a survey of 100 Frenchmen and constructed a confidence interval estimate of the unemployment rate, which of the following would be true? I) The center of the interval was 13.4. II) The interval contained 13.4. III) 99% confidence interval estimate contained 13.4. A. I and II B. I and III C. II and III D. I, II, and III E. None of the above gives the complete set of true responses.

15. 15)A photographer finds that 7% of all film processed by a certain company will be ruined. Find the probability that a random sample of 81 rolls of film processed by this company will contain at most 5% of the rolls that are ruined? • 0.2580 • 0.2611 • 0.2389 D. 0.2420 E. none of these

16. 16)Phil conducted a random survey of 1500 moviegoers and found that 650 of them really enjoyed a particular movie. Construct a 90% confidence interval for the true proportion of moviegoers that really enjoy the particular movie. • Between 41.2% and 45.4% • Between 40.8% and 45.8% • Between 58.8% and 54.6% D. Between 59.1% and 54.2%

17. 17) Which of the following are true statements? I) The P-value of a test is the probability of obtaining a result as extreme as the one obtained assuming the null hypothesis is true. II) If the P-value for a test is .015, the probability that the null hypothesis is true is .015. III) When the null hypothesis is rejected, it is because it is not true. • I only • II only • III only • I and III E. None of the above gives the complete set of true responses.

18. 18) Which of the following are true statements? I. The larger the P-value, the more evidence there is against the null hypothesis. II. The alternative hypothesis is stated in terms of a sample statistic. III. If a sample is large enough, the necessity for it to be a simple random sample is eliminated. • I only • II only C. III only D. Exactly two of the above statements are true. E. None of the above statements are true.

19. Multiple Choice Review – Chapters 18, 19, 20 • B 2)E 3) A • 4) B 5) A 6) D • 7) B 8) E 9) D • 10) B 11) B 12) D • 13) A 14) E 15) E • 16) A 17) A 18) E