6 - University of Florida



STA2023- Spring 2014 - Ripol EXAM 2 April 2, 2014

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.

• 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.

• YOU MUST SIGN, IN INK, the Honor Pledge on the next page of the exam and the back of the scantron sheet. The proctors will compare them to the signature on the ID.

• 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 answers on this test so you can compare your answers to the key that will be posted on the course website.

• This page contains Tables and Formulas. You may detach this page from the exam but make sure the rest of the exam does not fall apart!

|Case |parameter |estimator |standard error |Estimate of stderr |Sampling Distribution |

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

|one prop. | | |[pic] |CI:[pic] |z |

| |[pic] |[pic] | |ST:[pic] | |

STA2023- Spring 2014 - Ripol EXAM 2 TEST FORM A April 2, 2014

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

1. Which of the following have a sampling distribution?

a) [pic] and [pic] b) [pic] and p c) [pic] and [pic] d) [pic] and p e) [pic] and σ

2. What happens to the sampling distributions we studied in class if we increase the sample size, n?

i) The mean of the distribution gets closer to the desired value.

ii) The standard error decreases, resulting in a narrower and taller distribution.

iii) The shape of the distribution gets closer to Normal (if it wasn’t Normal to begin with).

a) Only (i) and (ii) are correct. b) Only (ii) and (iii) are correct.

c) Only (i) and (iii) are correct. d) All three statements are correct.

e) None of the three statements are correct.

3. Government statistics show that 8% of American adults are High School dropouts. We plan to take a random sample of 50 Americans and compute the proportion of dropouts in the sample. Can we find the probability that this sample proportion is more than 6%?

a) Yes, we could find that probability using the Z table.

b) Yes, we could find that probability using the t table.

c) No, we cannot find that probability because the sample size is too small.

d) We could find that probability after adding 2 successes and 2 failures to the sample.

e) We could find that probability after adding 11 successes and 12 failures to the sample.

4. Government statistics show that 8% of American adults are High School dropouts. We plan to take a random sample of 500 Americans and compute the proportion of dropouts in the sample. Find the probability that this sample proportion is more than 6%.

a) 0.9309

b) 0.9525

c) 0.4920

d) 0.0475

e) 0.0681

5. If we wanted to estimate the proportion of students who take the bus regularly to within .05 of the truth, with 95% confidence, how many students should be sampled? At least:

a) 382

b) 383

c) 384

d) 385

e) 386

6. A survey of college students asked how much money they spent on their last haircut appointment, including washing, styling, coloring and any other treatments received that day for their hair. For the 14 male students in the sample, the average cost was $14.07 with a standard deviation of $3.56. What would be the margin of error for the 95% confidence interval for the parameter based on this data?

a) 7.69

b) 2.13

c) 0.95

d) 2.16

e) 2.06

7. Are the assumptions are necessary for this confidence interval to be valid satisfied?

a) Yes, both the SRS and Normal distribution assumption are clearly satisfied.

b) It’s not clear if the sample was really random but it’s possible the data came from a Normal distribution.

c) The data seems reasonable random, but the assumption of Normality is clearly violated.

d) Both the assumptions of randomness and Normality are clearly violated so we shouldn’t interpret the interval.

e) There is no way to determine if there are any problems with either of these assumptions.

8. If we wanted to estimate the average cost of a haircut appointment for all male students to within $1 of the true amount, with 95% confidence, how many male students should be sampled? At least:

a) 84

b) 62

c) 49

d) 31

e) 42

9. For the 18 females in the sample, the average amount spent on their last haircut appointment was $46.10 with a standard deviation of $34.63. A confidence interval made with this data would be:

a) just as reliable as the one made for males because the data was collected by the same person.

b) more reliable than the one made for males because the sample size is larger.

c) less reliable than the one made for males because the distribution is definitely skewed.

d) less reliable than the one made for males because the standard deviation is larger.

e) more reliable than the one made for males because the mean is larger.

A 95% confidence interval was made for the average cost of a haircut appointment using data for all 32 males and females combined: (24.39, 43.79). Assuming all necessary conditions are satisfied, determine if the following interpretations are True or False.

|10. |95% of all students spend between $24 and $44 at their haircut appointments, on average. |a) True b) False |

|11. |We are 95% confident that the average amount spent by all 32 students at their haircut |a) True b) False |

| |appointments is between $24 and $44. | |

|12. |The probability that [pic]is between $24 and $44 is 0.95. |a) True b) False |

|13. |The probability that [pic] is between $24 and $44 is 0.95. |a) True b) False |

|14. |We are 95% confident that the average amount spent by all students in the population at their |a) True b) False |

| |haircut appointments is between $24 and $44. | |

15. What is the z value that should be used for an 85% confidence interval?

a) 1.44

b) 1.04

c) 0.8023

d) 1.58

e) It’s impossible to make an 85% confidence interval.

16. If the results of a significance test are statistically significant at α = 0.05 then:

a) we fail to reject Ho at α = 0.05

b) the p-value was smaller than 0.05

c) we have pretty strong evidence for Ho

d) all of the above

e) none of the above

17. If the p-value of a test is 0.073 then:

a) we can reject the null hypothesis at α =0.10 but not at 0.05 or 0.01

b) we can reject the null hypothesis at α =0.01 and 0.05 but not at 0.10

c) we can reject the alternative hypothesis at at α =0.10 but not at 0.05 or 0.01

d) we can reject the alternative hypothesis at α =0.01 and 0.05 but not at 0.10

e) we can reject the alternative hypothesis at α =.10 and the null at α =.01

18. We check that both np and n(1-p) are at least 15 to determine if the distribution of ____ is approximately Normal.

a) the sample b) the sample proportion

c) the population d) the population proportion e) the parameter

19. According to the latest US Department of Education data, yearly average cost of college tuition in 4-year institutions (including room and board) is $23,000 with a standard deviation of $9,500. We will take a random sample of 10 colleges and compute the average cost for the colleges in our sample. We cannot find probabilities about this sample mean because:

a) college costs in the sample do not have a Normal distribution.

b) college costs in the population do not have a Normal distribution.

c) the sample mean does not have a Normal distribution.

d) the population mean does not have a Normal distribution.

e) both b) and c) are correct.

20. According to the latest US Department of Education data, yearly average cost of college tuition in 4-year institutions (including room and board) is $23,000 with a standard deviation of $9,500. We will take a random sample of 30 colleges and compute the average cost for the colleges in our sample. Find the probability that this sample mean is less than $20,000.

a) 0.1720

b) 0.0418

c) 0.6255

d) 0.9573

e) 0.3745

Dentists recommend that, in addition to brushing our teeth at least twice a day, we should all floss daily - but what percentage of people actually do this? A random sample of 500 American adults was selected and they were asked how often they floss: 258 reported that they floss daily.

21. Construct a 95% confidence interval for the proportion of Americans who floss daily.

a) (0.47, 0.56)

b) (0.49, 0.54)

c) (0.48, 0.58)

d) (0.47, 0.59)

e) (0.44, 0.54)

22. Based on this confidence interval we can say that the proportion of Americans who floss daily:

a) is exactly 50% b) could be 50%

c) is not 50% d) is less than 50% e) is more than 50%

23. If we want to determine if the majority of American adults floss daily we should write the hypotheses as:

a) Ho: p =.5 Ha: [pic]= .516 b) Ho: [pic]=.516 Ha: p = .5

c) Ho: [pic]=.516 Ha: [pic] > .516 d) Ho: p =.5 Ha: p > .5 e) Ho: [pic]=.5 Ha: [pic] > .5

Match the following symbols with their value for this test:

24. p a) 258

25. [pic] b) 0.5

26. p0 c) 0.516

27. x d) 500

28. n e) unknown

29. Is the sample size large enough to conduct this test?

a) Yes, there are more than 30 people in the sample. b) Yes, since 258 and 242 are both larger than 15.

c) Yes, since 250 is larger than 15. d) Yes, since 258, 151 and 91 are all larger than 15.

e) Yes, since the original distribution is Normal.

30. The standard error of the test statistic for this problem is:

a) .0005 b) .0224

c) 124.9 d) 11.17 e) .7273

31. Data from the same survey was used to test if the proportion of Americans who never floss at all is less than 20%. The test statistic was computed to be -1.01. What is the p-value for this test?

a) 0.1562

b) 0.1357

c) 0.3143

d) 0.2714

e) 0.4857

32. Based on this p-value, there is ________ evidence to determine that the proportion of Americans who never floss at all is less than 20%.

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

33. The p-value for a two sided test to determine if the proportion of Americans who never floss at all is different from 20% would be:

a) twice as big as the p-value for the one-sided test above, making it harder to reject the null hypothesis.

b) twice as big as the p-value for the one-sided test above, making it easier to reject the null hypothesis.

c) half as big as the p-value for the one-sided test above, making it harder to reject the null hypothesis.

d) half as big as the p-value for the one-sided test above, making it easier to reject the null hypothesis.

e) the same as the p-value for the one-sided test above, making it just as easy to reject the null hypothesis.

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