STA 2023 - University of Florida



STA 2023 Name___________________________________

Spring 2012 UFID # ___________________ section_______

EXAM 3 Test Form Code D

Instructions:

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. One point will be given for correctly bubbling in the scantron your personal information and test form code.

You may write whatever you want on this test, but only the answers bubbled in the scantron sheet will be graded. This test MUST BE SUBMITTED to the instructors together with the scantron sheet for you to receive a grade on the exam.

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

Signature: ______________________________

Questions 1 – 5 As part of a science project, an elementary school student decided to study the amount of sugar in different types of chewing gum. Several brands of chewing gum (none with artificial sweeteners) were selected at the store, and each was categorized as either “kid” type of gum or “adult” type of gum. For each brand, a piece of gum was first weighted in its wrapper, and the gum was then chewed until all the flavor was dissolved. Then it was replaced in its wrapper and its weight was measured again. Since the only part that dissolves in saliva is the sugar, the difference in weight is the amount of sugar in each piece of gum.

Each of the five situations below describes an inference that we would like to make about a different parameter. Match each of the five situations below with the parameter of interest from the list. a) one mean

b) one proportion

c) difference of two dependent means

d) difference of two independent means

e) difference of two independent proportions

__1. Comparing the weight of each piece of gum before and after chewing.

__2. Determining the average sugar content for all the brands.

__3. Comparing the average amount of sugar for kid and adult type of gum.

__4. Noting that, at the store, 28 out of the 47 brands of gum available were “kids” gum.

__5. Noting that, at the store, 3 out of the 28 kids gum had artificial sweeteners, compared with

15 out of the 19 “adult” type gum.

6. When conducting a significance test to determine if there is a difference between two treatments, how do we summarize the data if we have a quantitative response variable, treatments are given to different experimental units?

a) compute the proportion of the sample that reacted better to treatment 1 than treatment 2.

b) compute the mean and standard deviation of each treatment group separately.

c) compute the difference in the responses for each experimental unit under both treatments, and then find the mean and standard deviation of the differences.

d) compute the difference in the proportion of the sample that reacted better to treatment 1 and the proportion of the sample that reacted better to treatment 2.

e) compute the difference in the proportion of successes for treatment 1 and the proportion of successes for treatment 2.

Questions 7- 11 Students in the Honors sections of STA 2023 were given a questionnaire that asked questions about the students' and their parents' use of Facebook. Minitab analysis appears below.

7. Looking at the first p-value we can say that the average amount of time spent on Facebook every day:

a) by female students is not significantly different from 1.50 hours.

b) by male students is not significantly different from 1.75 hours.

c) by male and female students are not significantly different from each other.

d) all of the above

8. How many degrees of freedom should we use in finding the p-value for the first output if doing the problem by hand?

a) 15 b) 30 c) 44 d) 43 e) 39

9. To compare the proportion of moms and dads that have Facebook accounts:

a) we should make a confidence interval for the difference of two independent proportions.

b) we should conduct a significance test for the difference of two independent proportions.

c) we should analyze the data with McNemar’s test for dependent proportions.

d) we should compute and interpret the Relative Risk.

10. Which of the following statements is correct in describing the results for students that participated in the study?

a) They spend, on average, less than 2 hours on Facebook per day.

b) Less than half of their parents have Facebook accounts, with moms a bit more likely to have one.

c) The majority of students would “friend“ their parents, with girls a bit more likely to say yes.

d) All of the above.

11. Are the assumptions for these tests satisfied?

a) No – time spent on Facebook appears to be skewed.

b) No –data is not randomly selected from the population.

c) No – the sample sizes are too small for some of the tests.

d) No –there are multiple problems, as described in all of the above.

e) Yes – all the assumptions seem satisfied.

Two-Sample T-Test and CI: How many hours a day do you spend on Facebook?

gender N Mean StDev SE Mean

M 16 1.59 1.13 0.28

F 31 1.76 1.52 0.27

95% CI for difference: (-0.956, 0.627)

T-Test of difference = 0 (vs not =): T-Value = -0.42 P-Val= 0.677 DF=39

Test and CI for One Proportion: Does your Mom have a Facebook account?

Variable X N Sample p 95% CI

facebook-mom 22 46 0.478261 (0.333907, 0.622615)

Test and CI for One Proportion: Does your Dad have a Facebook account?

Variable X N Sample p 95% CI

facebook-dad 15 44 0.340909 (0.200849, 0.480969)

Test and CI for Two Proportions: Are you/would you be “Friends” with them?

gender X N Sample p

M 10 16 0.625000

F 22 29 0.758621

95% CI for difference: (-0.417395, 0.150153)

Test for difference = 0 (vs not = 0): Z = -0.92 P-Value = 0.356

Questions 12 – 15 Have attitudes towards marijuana changed in your lifetime? The GSS asks almost every year: “Should marijuana be made legal?” In 2006, 35% (649 out of 1853) said yes, while in 1990, 16% (142 out of 863) said yes. The 95%CI for the difference p2006 – p1990 is: (0.1528, 0.2186)

12. Based on this confidence interval we can be 95% confident that:

a) the proportion of Americans in the sample that believes marijuana should be made legal has increased between 15% and 22% between 2006 and 1990.

b) the proportion of Americans in the population that believes marijuana should be made legal has increased between 15% and 22% between 2006 and 1990.

c) the proportion of Americans in the sample that believes marijuana should be made legal has either decreased by 15% or increased by 22% between 2006 and 1990.

d) the proportion of Americans in the population that believes marijuana should be made legal has either decreased by 15% or increased by 22% between 2006 and 1990.

13. What is the pooled p-hat that we would use in the significance test?

a) (142/649) + (863/1853) b) (649/1853) + ( 142/863)

c) (649+142) / (1853+863) d) (649/863) + ( 142/1853)

14. When interpreting the results of this study we should be concerned about:

a) the randomness of the data, which should be questioned and investigated further.

b) the data possibly not being Normally distributed, which would invalidate the results.

c) the organization conducting the study, which may be trying to elicit a particular response.

d) the fact that the topic of the question is sensitive, and people may be inclined to lie.

e) all of the above.

15. Which of the following is the correct interpretation of the Relative Risk for this problem? The proportion of Americans that believe marijuana should be legalized:

a) was 16% in 1990.

b) was 35% in 2006.

c) is 19% higher in 2006 than in 1990.

d) is 2.13 times higher in 2006 than in 1990.

e) all of the above

Questions 16– 19 How do average prices of new textbooks compare at the UF and Florida Bookstore? A random sample of 30 books was selected and the 95% CI for [pic] constructed: (2.05, 7.74)

16. This interval shows that, at α=0.05, average prices at the UF bookstore are __________ than those at the Florida Bookstore.

a) cheaper b) more expensive

c) significantly cheaper d) significantly more expensive

17. Based on the confidence interval what can we say about the p-value of a two-sided test to see if average prices are different?

a) p-value > 0.05 b) p-value < 0.05 c) p-value > 0.95 d) p-value < 0.95

18. A Type I error here would be determining that average prices on new textbooks at these two stores:

a) are different, when in fact they are not. b) are not different, when in fact they are.

c) are different, when in fact they are. d) are not different, when in fact they are not.

19. Based on the confidence interval what can we say about the p-value of a one-sided test to see if prices are more expensive, on average, at the UF bookstore?

a) p-value > 0.005 b) p-value = 0.045 c) p-value < 0.025 d) p-value > 0.10

Questions 20 – 24 A group of students, as part of a class project, asked International and American students living in Weaver Hall at UF how many hours they spent each week, on average, watching TV and shows on the Internet. They obtained a complete roster of every student living in Weaver Hall from an RA, assigned a number to each person and put the numbers into a box, then selected their participants. Boxplots of the data showed three high outliers in the International group.

Two-Sample T-Test and CI:

Sample N Mean StDev SE Mean

International 15 12.0 16.8 4.3

American 20 9.83 8.04 1.8

95% CI for difference: (-7.69, 12.03)

T-Test of difference = 0 (vs not =): T-Value = 0.46 P-Value = 0.650 DF = 18

T-Test of difference = 0 (vs ): T-Value = 0.46 P-Value = 0.325 DF = 18

20. What are the conclusions we can draw from this analysis?

a) The confidence interval shows significant differences, but the test does not.

b) The test shows significant differences, but the confidence interval does not.

c) Both the test and confidence interval show significant differences.

d) Neither the test nor confidence interval show significant differences.

21. We can comfortably extend our conclusions:

a) to all UF students.

b) to all Weaver Hall residents.

c) to all American and International students in the US.

d) to all students in the US and abroad.

22. Are there any problems with the assumptions necessary for this test to be valid?

a) Yes – we do not have enough successes and failures to perform the test.

b) Yes – there seems to be a problem with the assumption of Normal distribution.

c) Yes – students were not randomly selected.

d) Yes – all of the above are true.

e) No – all the assumptions seem satisfied.

23. The original question this group wanted to answer was whether International students spend less time watching shows, on average, than American students. Which of the following is the correct alternative hypothesis for this test?

a) Ha: [pic]< 0 b) Ha: [pic]> 0

c) Ha: [pic]< 0 d) Ha: [pic]> 0

24. This study found ___________ to prove International students spend less time watching shows, on average, than American students.

a) some evidence b) very strong evidence

c) not enough evidence d) no evidence at all e) inconclusive evidence

25. When testing Ho: [pic] = 0 vs Ha: [pic][pic]0 you get a p-value of 0.07. What can you say about the 99% CI based on the same data?

a) It will include 0.07 b) It will not include 0.07 c) It will not include 0.01.

d) It will include 0 e) It will not include 0

26. P-values are sometimes called “observed significance level”. That's because they represent:

a) the smallest α at which we can reject Ho b) the smallest α at which we can reject Ha

c) the biggest α at which we can reject Ho d) the biggest α at which we can reject Ha

Questions 27 – 28 A random sample of 15 college students was asked for their mother's age to test Ho: µ = 45 vs Ha: µ < 45. The test statistic was -1.758.

27. This test statistic implies that:

a) the sample mean was smaller than 45.

b) the sample mean was larger than 45.

c) the sample size was too small to do the test.

d) the sample size was large enough to do the test.

28. What is the p-value for this test?

a) 0.050 < p-val < 0.100 b) 0.100 < p-val < 0.200

c) 0.025 < p-val < 0.050 d) 0.010 < p-val < 0.025 e) 0.001 < p-val < 0.005

Questions 29 – 30 A study asked a random sample of 77 UF students whether they had download any copyrighted materials over the internet during the past month, and whether they believed laws regarding this practice are unfair. We will analyze this data with McNemar’s test for dependent proportions.

Have you downloaded copyrighted material in the last month?

|Are laws unfair? |Yes |No |

|Yes |33 |15 |

|No |20 |9 |

29. What are the null and alternative hypotheses for this test?

a) Ho: [pic]= 0 Ha: [pic][pic] 0 b) Ho: [pic]= 0 Ha: [pic][pic] 0

c) Ho: [pic]= 0 Ha: [pic][pic] 0 d) Ho: [pic]= 0 Ha: [pic][pic] 0

30. The p-value for the test was 0.84. Then we can say that the proportion of UF students that have downloaded copyrighted materials and the proportion that believes the laws are unfair:

a) are significantly different from each other in this sample.

b) are not significantly different from each other in this sample.

c) are significantly different from each other in the population.

d) are not significantly different from each other in the population.

31. If the test statistic for a test is -1, then the p-value will be:

a) large, regardless of whether we use the Z or t tables.

b) small if the test is about dependent samples, but large if they are independent.

c) large if the test is about proportions, but small if it is about means.

d) small, regardless of whether we do a confidence interval or significance test.

e) large if the test is two-sided, but small if it is one-sided.

32. A CI that includes zero can help us determine significance when we make inferences about:

a) proportions instead of means

b) independent instead of dependent samples

c) the difference of two groups instead of just one

d) population parameters instead of sample statistics

e) all of the above

33. We need to assume random samples any time we:

a) do inferences about means b) use the Z table

c) do inferences about proportions d) use the t table e) all of the above

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