讲解 ECMT1010 Introduction to Economic Statistics EXAMINATION Semester 1 - Main, 2017讲解回归

Economics

EXAMINATION

Semester 1 - Main, 2017

ECMT1010 Introduction to Economic Statistics

30 Multiple Choice Questions [ 15 marks total—suggested time approx. 32 minutes].

Use the following to answer questions 1–7. The following table displays descriptive statistics for the amount of ﬁnancialaid (in thousands of dollars) awarded to a sample of students at a large university.

n	x	s	min	Q1	m	Q3	max
120	15.142	7.362	3.400	9.925	13.500	19.275	35.000

1. Based on the information in the table, which of the following most likely describes the shape of the distribution of ﬁnancialaid amounts?

A) slightly skewed to the left

B) roughly symmetric

C) slightly skewed to the right

D) bell-shaped

E) uniform.

2. Based on the information in the table, which of the following intervals contains the 15th percentile of the distribution of ﬁnancialaid amounts (in thousands of dollars)?

A) 3.400 to 9.925

B) 9.925 to 13.500

C) 13.500 to 19.275

D) 19.275 to 35.000

E) none of the above

3. Based on the information in the table, give an interval that is certain to contain the 60th percentile of the distribution of ﬁnancialaid amounts (in thousands of dollars).

A) 3.400 to 9.925

B) 9.925 to 13.500

C) 13.500 to 19.275

D) 19.275 to 35.000

E) none of the above

4. Based on the information in the table, what is the range of ﬁnancial aid amounts (in thousands of dollars)?

A) 4.675

B) 9.35

C) 18.7

D) 31.6

E) 63.2

5. Based on the information in the table, what is the IQR of ﬁnancial aid amounts (in thousands of dollars)?

A) 4.675

B) 9.35

C) 18.7

D) 31.6

E) 63.2

6. Based on the information in the table, which of the following ﬁnancial aid amount(s) (in thousands of dollars) is/are an outlier/outliers?

A) 0

B) 35

C) 0 and 35

D) 30 and 35

E) 20, 30 and 35

7. Based on the information in the table, compute the z-score for the smallest ﬁnancialaid amount.

A) -2.37

B) -1.59

C) -0.22

D) 2.70

E) 2.92

Use the following to answer questions 8–11. The admissions staff at a small university want to use data from the past few years to predict the number of students enrolling in the university on the basis of the number accepted by the university. The data are provided in the following table.

Year	Number accepted	Number enrolled
2007	2,440	611
2008	2,800	708
2009	2,720	637
2010	2,360	584
2011	2,660	614
2012	2,620	625

8. Which of the following classiﬁcations is valid?

Explanatory variable Response variable

A) Year Number accepted

B) Year Number enrolled

C) Number enrolled Year

D) Number accepted Number enrolled

E) Number enrolled Number accepted

9. What is the sample mean of the number of students accepted?

A) 2560

B) 2581

C) 2600

D) 2640

E) 2660

10. What is the sample standard deviation of the number of students enrolled?

A) 38.49

B) 41.33

C) 42.17

D) 1481.81

E) 1778.17

11. What is the sample correlation between the number of students accepted and enrolled?

A) -0.83

B) -0.24 C) 0

D) 0.24

E) 0.83

Use the following to answer questions 12–17. Your friend Donald is often late for meetings. To prove a point, you want to study μ, the mean time Donald is late for meetings. The following table contains the minutes by which Donald is late for 7 random meetings (a negative value means Donald was early).

10 13 70 -5 8 38 27

12. What is , the mean time that Donald is late?

A) 13 B) 20 C) 21 D) 23 E) 27

13. To study how accurately x approximates μ, you decide to use the bootstrap. Which of the following is a valid bootstrap sample?

A) {38, 38, 38, 38, 38, 38, 38}

B) {10, 13, 70, 8, 8, -5, 70, 8}

C) {27, 27, 10, 10, -5, -6, 13}

D) {1, 2, 3, 4, 5, 6, 7}

E) {38, 70, 13, 10, 8, -5}

14. Using StatKey, you obtain the following bootstrap distribution of sample means:

Using the 95% rule, what is the 95% conﬁdence interval for μ?

A) (-0.3, 57.3)

B) (4.1, 46.6)

C) (5.5, 40.4)

D) (9.6, 38.1)

E) (14.3, 31.7)

15. Which of the following is most likely the 99% conﬁdence interval for μ?

A) (-0.3, 57.3)

B) (4.1, 46.6)

C) (5.5, 40.4)

D) (9.6, 38.1)

E) (14.3, 31.7)

16. Which of the following is most likely the 90% conﬁdence interval for μ?

A) (-0.3, 57.3)

B) (4.1, 46.6)

C) (5.5, 40.4)

D) (9.6, 38.1)

E) (14.3, 31.7)

17. To get a more accurate estimate of μ, you want to have a much lower standard error for the bootstrap distribution. Which of the following can help you achieve this?

A) Increase the number of bootstrap samples to 10,000.

B) Use a more powerful computer for bootstrapping.

C) Measure and record the times Donald is late for work for a year and bootstrap on this larger sample.

D) Get Donald to randomly meet his wife 30 times, record the time he is late and bootstrap on this larger sample.

E) Randomly meet Donald 30 more times, record the timeshe is late and bootstrap on this larger sample.

Use the following to answer questions 18–21. Let A and B be two events such that P (A) = 0.35, P (B) = 0.45 and P(A and B) = 0.1575.

18. Find P(not A).

A) 0.35

B) 0.45

C) 0.55

D) 0.65

E) 0.85

19. Find P(A or B).

A) 0.1000

B) 0.1575

C) 0.6425

D) 0.8000

E) 0.9575

20. Find P(BjA).

A) 0.1000

B) 0.1575

C) 0.3663

D) 0.4500

E) 1.2286

21. Which of the following description about events A and B are correct?

A) A and B are complementary.

B) A and B are mutually exclusive and independent.

C) A and B are NOT mutually exclusive and NOT independent.

D) A and B are mutually exclusive but NOT independent.

E) A and B are independent but NOT mutually exclusive.

Use the following to answer questions 22–25. There are three rooﬁng companies that service a small community. Al’s Roof Repair gets 45% of the rooﬁng jobs in the community while Bob’s Better Building and Carl’s Roof Service get 25% and 30% of the business, respectively. Of Al’s customers, 70% are satisﬁed. Of Bob’s customers, 95% are satisﬁed. Among Carl’s customers, 90% are satisﬁed.

22. What is the probability that a randomly selected customer used Al’s Roof Repair and is not satisﬁed?

A) 0.135

B) 0.165

C) 0.300

D) 0.315

E) 0.667

23. What is the probability that a randomly selected customer used Bob’s Better Building and is satisﬁed?

A) 0.0125

B) 0.2375

C) 0.2661

D) 0.7125

E) 0.9500

24. What proportion of rooﬁng customers are satisﬁed?

A) 0.1775

B) 0.5500

C) 0.8225

D) 1.0000

E) 2.5500

25. If a randomly selected customer is satisﬁed, what is the probability that they used Al’s Roof Repair?

A) 0.3150

B) 0.3830

C) 0.4500

D) 0.5471

E) 0.8511

Use the following to answer questions 26–30. Tony, the owner of a small auto repair store, wants to open a second store in Penrith, but will do so only if more than half of Penrith’s households have cars (otherwise there won’t be enough business). He sampled 300 households in Penrith and found that 165 have cars. Let p be the population proportion of car-owning households in Penrith.

26. What are the null and alternative hypotheses that summarize Tony’s decision?

A) H0 : p = 0, Ha : p > 0

B) H0 : p = 0, Ha : p > 0.5

C) H0 : p(ˆ) = 0, Ha : p(ˆ) > 0.5

D) H0 : p(ˆ) = 0.5, Ha : p(ˆ) > 0.5

E) H0 : p = 0.5, Ha : p > 0.5

27. What are the consequences of Type I and Type II errors in this case?

Type II error

A) Don’t open a 2nd store; miss out on a good business opportunity

B) Don’topen a 2nd store; avoid a bad business mistake

C) Open a 2nd store; get insufﬁcient business

D) Open a 2nd store; get insufﬁcient business

E) Don’topen a 2nd store; avoid a bad business mistake

Type II error

Open a 2nd store; get insufﬁcient business

Open a 2nd store; reap the beneﬁts of a good business

Don’t open a 2nd store; miss out on a good business opportunity

28. Tony obtained a bootstrap distribution of sample proportions of car-owning households in Penrith with a standard error of 0.03. What is the 95% conﬁdence interval for p?

A) (0.42, 0.48)

B) (0.48, 0.62)

C) (0.49, 0.61)

D) (0.52, 0.58)

E) It cannot be determined with the given information.

29. How can Tony generate a randomization distribution in this situation?

A) Mark each of the 300 answers (with or without car) on individual cards. Shufﬂe the cards and draw with replacement 300 times. Find the proportion of times getting a ‘with cars’ card. Repeat 10,000 times.

B) Mark each of the 300 answers (with or without car) on individual cards. Shufﬂe the cards and draw without replacement 300 times. Find the proportion of times getting a ‘with cars’ card. Repeat 10,000 times.

C) Ask the same 300 households the same question again on another day, and record the propor- tion of having cars. Repeat 10,000 times.

D) Ask a different group of 300 households the same question, and record the proportion of having cars. Repeat 10,000 times.

E) Toss a fair coin 300 times independently and ﬁnd the proportion of tosses with a head facing up. Repeat 10,000 times.

30. A randomization distribution under the null hypothesis is shown below:

Tony solicited the help of some friends to form. a conclusion. Their answers are as follows.

Andrew: “Reject at the 5% signiﬁcance level.”

Eric: “Reject at the 2% signiﬁcance level.”

Joe: “Reject at the 1% signiﬁcance level.”

Based on the sample and the randomization distribution, who made the correct decision?

A) They are all wrong.

B) Only Andrew is correct.

C) Only Eric is correct.

D) Only Joe is correct.

E) Only Eric and Joe are correct.

Long Question 1 [20 marks total—suggested time approx. 44 minutes]

Using data on 24 inkjet printers for sale on The Good Guys website in April 2017, a researcher obtains the following regression output for a model used to predict printer price (measured in dollars) based on printing speed (measured in pages per minute, PPM).

Predictor Coefficient	SE coef .	t stat
Intercept 28 .5714	46 .2082	0 .6183
PPM 6 .0757	2 .1028	2 .8893
Regression statistics
R square 0 .2751	SD error	74.3863 Observations 24
Analysis of variance
Source df	SS
Regression 1	46,192 .22
Residual 22	121,733 .12
Total 23	167,925 .33