STA 2023 - University of Florida



STA2023- Spring 2016 - Ripol EXAM 3 April 23, 2016

FORMAT: This exam contains 33 Multiple Choice questions. Please select the best answer among the alternatives given. Each question is worth 3 points, for a total of 99 points. The last point will be awarded for correctly bubbling in your name, UFID number and Test Form Code on the scantron sheet and showing your GatorOne picture ID.

INSTRUCTIONS: Using a pencil, complete the exam questions and bubble in your answers on the scantron sheet. You may write whatever you want on this test, but only the answers bubbled in the scantron sheet will be graded. Make sure you mark all your final answers on this test so you can compare your answers to the key that will be posted on the course website.

COVER SHEET: This page contains Tables and Formulas you may use during the exam. You may detach this page from the exam but this page must be turned in to the proctors when you finish the exam, together with the scantron form, in order to receive credit for the exam.

CHECK EACH BOX TO CONFIRM THE FOLLOWING:

← I have written and bubbled in my NAME, UFID, and SECTION number on the SCANTRON sheet, using a pencil.

← I have bubbled in the TEST FORM CODE for my exam (which appears at the top of the next page) on the SCANTRON sheet, using a pencil.

← I have SIGNED the back of my SCANTON and the NEXT PAGE, in INK.

← I have READ and ABIDED by the HONOR CODE STATEMENT below.

"On my honor, I have neither given nor received unauthorized aid on this examination."

Sign your name in INK: _______________________________________

Print your full name: _______________________________________

UF ID: ______________________________

Section: ______________________________

STATISTICAL INFERENCE TABLE: McNemar [pic] OR [pic]

|Case |parameter |estimator |standard error |Sampling Distribution |

|one mean |[pic] |[pic] |[pic] |t (n-1) |

|mean of matched pairs |[pic] |[pic] |[pic] |t (n-1) |

|difference | | | | |

|difference |[pic] |[pic] |[pic] |t with |

|of two independent means | | | |conservative df = smallest of (n1-1) |

| | | | |and (n2-1) |

| | | | |“liberal” df = n1 + n2 - 2 |

|one proportion |[pic] |[pic] |CI:[pic] |z |

| | | |ST:[pic] | |

|difference |[pic] |[pic] |CI:[pic] |z |

|of two independent proportions| | |ST: [pic] | |

[pic]

STA2023- Spring 2016- Ripol EXAM 3 TEST FORM B April 23, 2016

Honor pledge: "On my honor, I have neither given nor received unauthorized aid on this examination."

Questions 1 – 5 A study published in Statistics in Medicine had several women try both low dose and high dose analgesics and report if they experienced relief of menstrual cramping. The results appear on the table.

High Dose

Low Dose Success Failure

|Success |53 | 8 | |

|Failure |16 |9 | |

1. What percentage of women in the study experienced relief with the low dose analgesic?

a) 64% b) 71% c) 77% d) 80% e) 87%

2. What percentage of women in the study experienced relief with the high dose analgesic?

a) 64% b) 71% c) 77% d) 80% e) 87%

3. Compute the Test Statistic for McNemar’s Test.

a) 1.63 or -1.63

b) 5.59 or -5.59

c) 1.63 or 5.59

d) 4.45 or -4.45

e) 5.59 or 4.45

4. The p-value for this test is 0.1032. Assuming all conditions necessary are satisfied, we can conclude that there is not enough evidence to prove:

a) that low dose analgesic relieves menstrual cramps.

b) that high dose analgesic relieves menstrual cramps.

c) that either high or low dose analgesic relieves menstrual cramps.

d) a difference in the effectiveness of high and low dose analgesics to relieve menstrual cramps.

e) that low dose analgesic relieves menstrual cramps, but we can prove that high dose relieves it.

5. We use McNemar’s Test to analyze this data because:

a) there were two separate groups of women receiving low and high dose analgesics.

b) the data reported is quantitative rather than categorical.

c) the assumptions necessary for independent means procedures are not satisfied.

d) the data reported was on dependent proportions.

e) None of the above

6. Concluding there is a significant difference between two population means is the same as saying:

a) There are differences in the population means that are large enough to be of importance.

b) There are differences in the sample means that are large enough to be of importance.

c) There are differences in the sample means, but they are not large enough to be of importance.

d) The difference in the population means was large enough to prove a difference in the sample.

e) The difference in the sample means was large enough to prove a difference in the population.

7. In conducting Significance Tests:

a) Type I errors are considered avoidable, but Type II errors are not.

b) Type II errors are considered avoidable, but Type I errors are not.

c) Both Type I and Type II errors are considered avoidable.

d) Both are unavoidable, but Type I errors are considered more serious than Type II errors.

e) Both are unavoidable, but Type II errors are considered more serious than Type I errors.

Questions 8 – 10 A recent GSS asked participants whether they agreed with the following statement: America should take stronger measures to exclude illegal immigrants. The 95% confidence interval for the difference in the percentage of women (1) and men (2) who agreed or strongly agreed with the statements was (-0.13, -0.02).

8. Based on this interval we are 95% confident that the proportion of women who agree or strongly agree with that statement in the _______ is between 2% and 13% _________ than the proportion of men who do the same.

a) sample, lower b) sample, higher c) population, lower d) population, higher e) none of those

9. If we wanted to determine whether the proportion of women who agree or strongly agree with that statement in the population is lower than the proportion of men who do the same we could conduct a significance test of:

a) Ho: p1-p2 = 0 vs Ha: p1-p2 < 0 b) Ho: p1-p2 = 0 vs Ha: p1-p2 >0

c) Ho: [pic]= 0 vs Ha: [pic]< 0 d) Ho: [pic]= 0 vs Ha: [pic]>0

e) none of the above

10. If we wanted to determine whether the proportion of women who agree or strongly agree with that statement in the sample is lower than the proportion of men who do the same we could conduct a significance test of:

a) Ho: p1-p2 = 0 vs Ha: p1-p2 < 0 b) Ho: p1-p2 = 0 vs Ha: p1-p2 >0

c) Ho: [pic]= 0 vs Ha: [pic]< 0 d) Ho: [pic]= 0 vs Ha: [pic]>0

e) none of the above

Questions 11-15 Getting a driver’s license has long been considered a rite of passage for teenagers, but this generation is waiting longer to do it. Some teens claim they can get around fine without a license, others cite the high cost of driving, and others say social media makes it easy to interact with friends without leaving home. Even though younger drivers have the highest rates of accidents, waiting to drive until you are older does not inherently make you a safer driver. The graduated licensing process that requires 15-17 year olds to drive with certain restrictions and adult supervision for their first year does not apply after age 18, which means older new licensees might be more inexperienced than younger ones. Match each of the five situations below with the parameter of interest from the list. (They can be used more than once).

a) one mean

b) one proportion

c) difference of two dependent means

d) difference of two independent means

e) difference of two independent proportions

11. In their first year of driving one in five 16-year-old drivers has an accident.

12. Teens in families with higher incomes were far more likely to get their licenses early than teens in low-income families. In families making $60,000 or more a year, 60 percent of teens got their licenses within a year of being eligible for one. In families making $20,000 or less, only 16 percent of teens got their licenses in that time frame.

13. A study conducted by the University of Michigan Transportation Institute suggests that only around 60 percent of those between the ages of 17 and 19 are licensed to drive, compared to 80 percent of teens back in the 1980’s.

14. For the average family, adding a teen driver almost doubles their car insurance rates.

15. The average cost of insuring a teen driver is considerably lower for females than males.

16. The fatality rate for drivers aged 16 to 19 is four times that of drivers aged 25 to 69 years. This statement is an example of:

a) McNemar’s test b) Relative Risk c) Type I error d) Type II error

e) none of the above

Questions 17 – 26 A recent GSS asked men and women how many close friends they have. We will compare the responses for participants aged 18 -25. The Minitab output of the analysis appears below.

Sample N Mean StDev SE Mean

Male 26 9.58 12.66 2.48

Female 34 4.38 2.93 0.50

95% CI for difference: (0.0029, 10.3971)

T-Test of difference = 0 (not =): T-Value = 2.053 P-Value = 0.0499 DF = 27

17. The standard deviation of the sampling distribution of [pic]1 - [pic]2 is:

a) 2.98 b) 1.41 c) 2.53 d) 1.98 e) 1.72

18. From the confidence interval we can conclude that males in this age group have, on average:

a) between 0. 29% and 10.4% more close friends than females.

b) between 0. 29% and 10.4% less close friends than females.

c) between 0.0029 and 10.3971 close friends.

d) between 0.0029 and 10.3971 more close friends than females.

e) between 0.0029 and 10.3971 less close friends than females.

19. We can determine whether there is a significant difference between the two groups by checking whether the confidence interval includes:

a) the alpha level b) the test statistic c) the p-value d) the estimator e) none of those

20. Based on the p-value we can Reject Ho at alpha levels of:

a) 0.10 and 0.05 b) 0.10 c) 0.01 d) 0.01 and 0.05 e) 0.05

21. Based on the p-value we can predict that a _____ confidence interval for the difference will not show significant differences.

a) 90% b) 95% c) 99% d) all of those e) none of those

22. The degrees of freedom used by the statistical computing program were 27. When doing this problem by hand we know the degrees of freedom are bounded by our conservative and liberal estimates of:

a) 26 and 34 b) 25 and 58

c) 25 and 33 d) 26 and 57 e) 25 and 33

23. Are there any problems with the assumptions for this statistical analysis?

a) Given the information in the problem, we are not sure if the samples were randomly selected.

b) It looks like there is a problem with the normal distribution of one of the populations given the sample size.

c) It looks like there is a problem with the normal distribution of both of the populations given the sample sizes

d) Given the information in the problem, we cannot check if there are enough successes and failures in the sample.

e) None of the above.

24. Suppose the original problem wanted to determine if the average number of close friends males have is different from females in the 18-25 age group. The p-value for this test would be:

a) 0.0499 b) 0.0998 c) 0.97505 d) 0.02495 e) 0.9501

25. Suppose the original problem wanted to determine if the average number of close friends males have is higher than females in the 18-25 age group. The p-value for this test would be:

a) 0.0499 b) 0.0998 c) 0.97505 d) 0.02495 e) 0.9501

26. Suppose the original problem wanted to determine if the average number of close friends males have is less than females in the 18-25 age group. The p-value for this test would be:

a) 0.0499 b) 0.0998 c) 0.97505 d) 0.02495 e) 0.9501

Questions 27 – 33 Modern tennis balls must conform to certain criteria for size, weight, deformation, and bounce to be approved for regulation play. The International Tennis Federation defines the official diameter as 6.54–6.86 cm with weight in the range 56.0–59.4 grams. Yellow and white are the only colors approved by the ITF, and most balls produced are a fluorescent yellow known as "optic yellow”, chosen for its high visibility on color television.

When it is operating correctly, a machine for manufacturing tennis balls produces balls with a mean weight of 57.6 grams. The last eight balls manufactured had weights that averaged 57.275 grams and a standard deviation of 0.1669 grams. We will use this sample to make inferences about µ.

27. The parameter of interest in this case is µ= the average weight of all tennis balls:

a) in the sample, that is, those last 8 balls manufactured, which is 57.275 grams.

b) in the population of balls ever produced by this machine, which is 57.6 grams.

c) in the population of balls being produced by this machine now, which is unknown.

d) in the population of balls that is approved for regulation play, which is 56.0–59.4 grams.

e) in the population of balls ever produced in the world, which is unknown.

28. Construct a 95% confidence interval for µ.

a) (57.18, 57.37)

b) (56.95, 57.60)

c) (57.14, 57.41)

d) (56.88, 57.67)

e) (57.23, 57.32)

29. What is the correct alternative hypothesis to test whether the machine is operating correctly?

a) Ha: µ ≠ 0

b) Ha: µ ≠ 57.6

c) Ha: µ ≠ 57.275

d) Ha: µ ≠ 56.0

e) Ha: µ ≠ 59.4

30. The test statistic was computed to be -5.51. We can tell the p-value for this test is approximately zero because:

a) this test statistic is so far from zero using the z table.

b) this test statistic is so far from zero using the t table.

c) this test statistic is so far from the value in Ho using the z table.

d) this test statistic is so far from the value in Ho using the t table.

e) all of the above

31. Since the p-value is almost zero we can conclude that there is:

a) very strong evidence to say the machine is operating correctly.

b) very strong evidence to say the machine is not operating correctly.

c) some evidence to say the machine is operating correctly.

d) some evidence to say the machine is not operating correctly.

e) not enough evidence to say the machine is operating correctly.

32. The results of the confidence interval for µ and the test to see if the machine is operating correctly:

a) must agree in this problem.

b) do not have to agree in this problem since it’s for one group instead of two.

c) do not have to agree in this problem since it’s for means instead of proportions.

d) do not have to agree in this problem since we have a small sample, not a large one.

e) do not have to agree in this problem since it’s for a parameter instead of a statistic.

33. If we consider whether the balls are of regulation size, we can say from this analysis that:

a) even though we have practical significance, there is no statistical significance.

b) even though we have statistical significance, there is no practical significance.

c) we have both statistical significance and practical significance.

d) we have neither statistical significance nor practical significance.

e) there is no way to prove practical significance in this study.

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