STA 2023 - University of Florida



STATISTICAL INFERENCE

STA2023- Spring 2013 - Ripol EXAM 3 TEST FORM A April 27, 2013

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

A study conducted by a group of UF students as part of a class project compared the average number of hours per week that Psychology and Engineering majors spend studying. The results appear below.

Sample N Mean StDev SE Mean

Psy 32 10.67 5.44

Eng 35 21.83 8.77 1.5

95% CI for difference: (-14.70, -7.62)

T-Test of difference = 0 (not =): T-Value = -6.32 P-Value = 0.000 DF = 57

1. This test is trying to determine if Psychology majors study ______ Engineering majors per week, on average.

a) less than b) ten hours less than c) a different amount than

d) more than e) ten hours more than

2. From the confidence interval we can conclude that Psychology majors study, on average :

a) between 7.62 and 14.70 hours per week.

b) between 7.62 and 14.70 hours per week more than Engineering majors.

c) between 7.62 and 14.70 hours per week less than Engineering majors.

d) between 7.62% and 14.70% more than Engineering majors.

e) between 7.62% and 14.70% less than Engineering majors.

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

a) zero b) the test statistic c) the p-value d) the estimator e) none of the above

4. Based on the p-value we can conclude that there is _________________ evidence of a difference in the average number of hours these two groups study per week.

a) very strong b) pretty strong c) some d) not enough e) not any

5. Based on the p-value we can predict that a _____ confidence interval for the difference will show significant differences.

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

6. The degrees of freedom used by the statistical computing program were 57. When doing this problem by hand we know the degrees of freedom are bounded by our conservative and liberal estimates of:

a) 31 and 67 b) 32 and 67

c) 31 and 34 d) 31 and 65 e) 31 and 66

7. Over 30 students from each major were sampled, so this guarantees that we have:

a) simple random samples

b) normal distribution of the statistic

c) normal distribution of the original populations

d) 15 successes and 15 failures per group

e) all of the above

8. The standard error of [pic]in this study is:

a) 5.44 b) 0.17 c) 0.96 d) 1.96 e) 2.72

9. Which of the following statements is true?

a) The confidence interval is a type of point estimate.

b) The center of a confidence interval is a population parameter.

c) The bigger the margin of error, the smaller the confidence interval.

d) A population mean is an example of a point estimate.

e) None of the above statements are true.

The New York Times (9/25/09) reported on a study that declared a vaccine against the HIV virus “a qualified success after a six-year clinical trial on more than 16,000 volunteers in Thailand”. The men and women were recruited from the general population rather than high risk groups. Half of the participants got the placebo (group 1) and the other half was given the vaccine (group 2). Everyone was given six doses of the treatment, all were offered condoms, taught to avoid infection and promised life-long antiretroviral treatment if they got AIDS. They were regularly tested for three years and in the end 74 of those who got placebos became infected but only 51 of those that got the vaccines did. The 95% CI for the difference of the two population proportions was (0.00013, 0.00541) and the p-value to prove the vaccine works better than the placebo was 0.020.

10. How should we write the alternative hypothesis to prove the vaccine works better than the placebo?

a) Ha: p d > 0 b) Ha: p d < 0 c) Ha: p 1 – p 2 > 0 d) Ha: p 1 – p 2 < 0 e) Ha: [pic]1 – [pic]2 < 0

11. Based on the confidence interval we can be 95% confident that the chance of becoming infected with the HIV virus is:

a) between 0.013% and 0.541% smaller for people that take the placebo than for people that take the vaccine.

b) between 0.013% and 0.541% larger for people that take the placebo than for people that take the vaccine.

c) between 0.013% smaller and 0.541% larger for people that take the placebo than for people that take the vaccine.

d) between 0.013% smaller and 0.541% larger for people that take the vaccine than for people that take the placebo.

e) between 0.013% smaller and 0.541% larger for people in the sample than for people in the population.

12. Do the results of the confidence interval and the significance test agree in this problem?

a) No, they don’t agree, but that can happen when the sample sizes are very large.

b) No, they don’t agree, but that can happen when the test is one sided.

c) Yes, they do agree, and both found significant differences in the two groups.

d) Yes, they do agree, and both found no significant differences in the two groups.

e) The results don’t quite agree, but they do agree once we double the p-value.

13. A Type I error in this problem would be:

a) Receiving the vaccine and getting infected. b) Receiving the placebo and not getting infected.

c) Saying the vaccine works when it really does not. d) Saying the vaccine does not work when it really does.

e) Saying a person is infected when they’re really not.

14. Which of the following statements is true about this problem?

a) This example verifies that statistical significance always implies practical significance.

b) This example verifies that practical significance always implies statistical significance.

c) We cannot conclude the vaccine works because correlation does not imply causation.

d) Even though a difference of 0.5% was statistically significant it may not be practically significant.

e) Even though a difference of 0.5% was practically significant it may not be statistically significant.

15. The sample proportion infected in the placebo group and the vaccine group are, respectively:

a) 13% and 54% b) 0.013% and 0.54% c) 74% and 51% d) 0.9% and 0.6%

16. The Relative Risk is a good statistic to compute in this problem because even though the difference in the two proportions is quite small, the chance of getting infected for the placebo group is about:

a) 42 times as large as the chance of getting infected for the vaccine group.

b) 1.45 times as large as the chance of getting infected for the vaccine group.

c) 23 times as large as the chance of getting infected for the vaccine group.

d) 77% higher than the chance of getting infected in the vaccine group.

e) 23% higher than the chance of getting infected in the vaccine group.

17. The Sampling Distribution of x-bar will be approximately Normal:

a) only if the population size is 30 or more

b) only if the sample size is 30 or more

c) only if the shape of the original distribution is Normal

d) only if the shape of the sample distribution is Normal

e) none of the above

In the TED Talk “What doctors don't know about the drugs they prescribe,” the speaker Ben Goldacre talks about the publication bias for drug trials that affects all fields of medicine, in which positive findings about drugs are published and negative or unflattering results tend to be “buried”.

18. Some studies about a drug may find an effect just by chance. These are referred to as:

a) Type I errors b) Type II errors

c) Relative Risk s d) McNemar’s Trials e) Not Practically Significant

19. The problem with this publication bias is that:

a) it’s hard to find out even how many total experiments have been conducted on a drug if only some are published.

b) the responsibility for this bias is diffused among researchers, academics, industry sponsors and journal editors.

c) doctors are misled into prescribing drugs based on only half of the experiments conducted.

d) all of the above

A growing number of people have stopped paying for cable and satellite TV service, and don't even use an antenna to get free signals over the air. They are watching shows and movies on the Internet, sometimes via cellphone connections. Last month, the Nielsen Co. started labeling people in this group "Zero TV" households, because they fall outside the traditional definition of a TV home. There are 5 million of these residences in the U.S., up from 2 million in 2007 and they make up about 5% of households in the US. Match each of the five situations below with the parameter of interest from the list. (They should be used only 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

____ 20. Though most (75%) Zero TV households still own at least one TV, they tend to use those sets to watch DVDs, play games, or browse the Internet.

____ 21. On average, Americans spend more than 41 hours each week—nearly five-and-one-half hours (5:28) daily—engaging with content across all screens.

____ 22. Viewing behavior varies by ethnicity, however: African-Americans spend close to 55 hours engaging on all screens, Hispanics just over 35 hours.

____ 23. Although pre-recorded programs are more popular now than ever, people still watch, on average, around 4 hours more live TV per day than time-shifted programming.

____ 24. Zero TV homes tend to be younger, with 45% of them having a head-of household under the age of 35, compared to 18% for more traditional homes.

25. Using McNemar’s Test to analyze categorical data for two independent groups would give results that are:

a) consistent with those of the confidence interval for the difference of two proportions

b) consistent with those of the significance test for the difference of two proportions

c) consistent with those of the confidence interval for the relative risk

d) all of the above

e) completely inappropriate for this data

26. When testing Ho: p =.75 vs Ha: p < .75 the sample proportion of successes turns out to be 0.77. The p-value for this test is:

a) greater than 0.50 b) smaller than 0.50

c) equal to 0.50 d) equal to 0.02

e) impossible to determine

The table that follows refers to a sample of juveniles convicted of a felony in Florida. Matched pairs were formed using criteria such as age and the number of prior offenses. For each pair, one subject was handled in the juvenile court system and the other was transferred to the adult court. The response of interest is whether the juvenile was rearrested within a year. We will analyze this data with McNemar’s test for dependent proportions.

Juvenile Court

Adult Court Rearrest No Rearrest

|Rearrest |158 |515 |673 |

| No Rearrest |290 |1134 |1424 |

448 1649

27. The sample proportion of rearrest for the juvenile and adult courts are:

a) 35% and 23% respectively.

b) 23% and 35% respectively.

c) 32% and 21% respectively.

d) 21% and 32% respectively.

e) unknown, and cannot be estimated form this data.

28. The hypotheses for this test are statements about:

a) pd b) p c) [pic] d)[pic] e) [pic]

29. Compute the test statistic.

a) 27.15 b) 15.24 c) 7.93 d) 6.23 e) 33.67

30. Using any of the possible test statistics above, the p-value of the test will be:

a) extremely small, so we find significant differences in the proportion of rearrest for the two courts.

b) extremely small, so we find no significant differences in the proportion of rearrest for the two courts..

c) extremely large, so we find significant differences in the proportion of rearrest for the two courts.

d) extremely large, so we find no significant differences in the proportion of rearrest for the two courts.

e) impossible to compute without more information.

31. For the Sampling Distribution of p-hat to be Normal we will need a larger sample size when:

a) p is very small b) p is very large

c) p is far from 0.5 d) p is close to 30 e) p is close to 0.5

32. Which of the following statements is true regarding the pooled proportion of successes.

a) It is used when comparing two independent proportions, but not for dependent ones.

b) It is computed by combining all the successes both groups over all the trials for both groups.

c) It is used in computing the standard error for the test statistic but not in the confidence interval.

d) It is the best estimate of the population proportion of successes under the null hypothesis of no difference.

e) all of the above

33. Statistical Inference procedures are conducted:

a) when we want to compare the sample statistic to the population parameter.

b) when we want to draw conclusions about a population based on a sample.

c) when the data we have does not satisfy all the assumptions.

d) all of the above

e) none of the above

34. When doing statistical inference, a larger sample size is desirable because it:

a) results in a wider confidence interval b) makes it easier to reject the null hypothesis

c) allows us to use the t table instead of the z table d) all of the above e) none of the above

35. Some companies claim to offer coaching courses that can improve your SAT scores. SAT Math scores in the absence of coaching have a mean of 475 points. After a very successful advertising campaign, a company gets 10,000 customers, whose average SAT Math score after coaching turns out to be 478 with a standard deviation of 100 points. We will use this data to construct a confidence interval for (, which represents the average SAT Math score:

a) for all students in the absence of coaching, which is 475 points.

b) for all students taking this course, which is 478 points.

c) for all students not taking this course, which is unknown.

d) for all students that could have taken this course, which is unknown.

e) for all students in the sample population, which is unknown.

The Freshman 15 is the name of a common belief that college students, particularly women, gain an average of 15

pounds during their first year of college. Data for 100 freshmen women was collected by recording their weights at the start and the end of the school year and the difference (wt.start-wt.end) computed for each one. There are parts of the output of several computer analyses below. Use them to answer the following questions.

36. How should the null and alternative hypotheses be written to see if there’s been any weight gain on average?

a) Ha: (d > 0 b) Ha: (d < 0

c) Ha: (d = 0 d) Ha: (d ≠ 0

e) none of the above

37. What’s the best conclusion we can draw from this data to all freshmen college women?

a) Although there is a significant weight gain during the first year, it’s really about 2-3 pounds on average, not 15.

b) Although there is a significant weight gain during the first year, it’s really about 5-11 pounds on average, not 15.

c) Strong evidence to say the average weight gain during the first year is not significantly different from 15 pounds.

d) Some evidence to say the average weight gain during the first year is not significantly different from 15 pounds.

e) Strong evidence to say the average weight gain during the first year is not significantly different from zero.

38. Which of the following statements is true about the assumptions necessary for the conclusions to be valid?

a) The women need to be a random sample of all female college freshmen.

b) We need to assume there are more than 30 women sampled for this study.

c) The data should have no women who weigh less than 100 pounds or over 170.

d) There should be at least 15 women who gained weight and 15 who lost weight in the sample.

e) All of the above are necessary.

Summary Statistics

N Mean StDev SE Mean

wt.start 100 134.49 30.85 3.08

wt.end 100 137.23 30.81 3.08

Difference 100 -2.742 2.146 0.215

Two-Sample T-Test and CI: wt.start wt.end

95% CI for difference: (-11.34, 5.86)

T-Test of difference = 0 (vs not =): T-Value = -0.63 P-Value = 0.530 DF = 197

Paired T-Test and CI: wt.start wt.end

95% CI for mean difference: (-3.168, -2.316)

T-Test of mean difference = 0 (vs not = 0): T-Value = -12.78 P-Value = 0.000

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