MidtermEconomics 173Name______

Fall 2001Instructor: PetrySSN______

  1. The following table presents the summary statistics from a sample of 24 exam scores, expressed in percentages.

Score
Mean / 75.67
Standard Error / 1.782226
Median / 73
Mode / 73
Standard Deviation / 8.731087
Sample Variance / 76.23188
Kurtosis / 0.646501
Skewness / 1.303676
Range / 30
Minimum / 66
Maximum / 96
Sum / 1816
Count / 24
Confidence Level(95.0%) / 3.68681

In order to do a test where the null hypothesis specifies the population mean exam score to be equal to 72,

  1. the t-distribution should be used to get a test statistic equal to 10.09
  2. the z-distribution should be used to get a test statistic equal to 10.09
  3. not enough information is given to calculate the test statistic
  4. a pooled variance t-test should be used.
  5. The t-distribution should be used to get a test statistic equal to 2.06

2. Based on a 95 % confidence interval, if you tested H0: μ = 72, H1: μ  72, you would:

  1. not be able construct the confidence interval due to lack of information.
  2. Fail to reject the null hypothesis
  3. Reject the null hypothesis
  4. Reformulate a one sided hypothesis instead.

3. What is the median salary (in thousands) of the following array: 25 29 38 41 46 66

  1. 29
  2. 38
  3. 39.5
  4. 46.7
  5. 66

4. The standard deviation is:

  1. 2 times the variance
  2. the square root of the variance
  3. the absolute value of the variance
  4. the variance squared
  5. none of the above

5. Find the standard deviation (in years) of the following array: 3, –2, –4, 1, 0, –1, 2

  1. 1.3
  2. 1.75
  3. 1.275
  4. 2.95
  5. 2.41

6. If two variables are strongly and negatively correlated, the coefficient value will be close to:

  1. 0
  2. 0.8
  3. –1
  4. 1
  5. 0.2

7. What is the 90% confidence interval (Z= 1.645), for a mean of 5.2, a population standard deviation of 2, and a sample of 60:

  1. 4.0651, 5.5554
  2. 4.1622, 5.4377
  3. 4.9749, 5.8846
  4. 4.2432, 5.5094
  5. 4.7753, 5.6247

8. One way of decreasing the width of the interval estimator is:

  1. increasing the sample size
  2. changing the test statistic
  3. changing the mean, variance and standard deviation
  4. using a different p-value
  5. None of the above

9. What sample size is required for a machine to be precise within 0.8 inches with 90% confidence (Z = 1.645)? Assume population is normally distributed, with a population standard deviation of 3.

  1. 36
  2. 37
  3. 38
  4. 39
  5. 40

10. Given the following p-values and their associated Z-scores, what is the last entry in the table?

P-value / Z-statistic
0.02275 / 2
0.049985 / 1.645
0.024998 / 1.96
0.158655 / 1
0.284339 / 0.57
0.096801
  1. 0.3
  2. 0.8
  3. 1.3
  4. 1.8
  5. 2.3

11. Students claim that the grading in Underwater Basket Weaving 101 is harsher during the fall semester than during the spring. To back up their claim, they obtained the scores of last fall and spring. At a 5% significance level, what is your decision?

t-Test: Paired Two Sample for Means / t-Test: Two-Sample Assuming Equal Variances
t Stat / -3.58581 / t Stat / -0.65389
P(T<=t) one-tail / 0.002939 / P(T<=t) one-tail / 0.261237
t Critical one-tail / 1.859548 / t Critical one-tail / 1.745884
P(T<=t) two-tail / 0.005877 / P(T<=t) two-tail / 0.522473
t Critical two-tail / 2.306006 / t Critical two-tail / 2.119905
  1. Reject the null, conclude there is sufficient evidence that the grades are different.
  2. Reject the null, conclude there is not sufficient evidence that the grades are different.
  3. Fail to reject the null, conclude there is sufficient evidence that the grades are different.
  4. Fail to reject the null, conclude there is insufficient evidence that the grades are different.
  5. All of the above.

12. If the two sided test produces a test statistic of -1.8 and a p-value of .15, what is your conclusion if you make it a one sided test with the alternative H1: u < 0 at a 10% significance level?

  1. Reject the null: there is enough evidence to conclude that the mean is less than zero.
  2. Reject the null: there is not enough evidence to conclude that the mean is less than zero.
  3. Fail to reject the null: There is not enough evidence to conclude the mean is less than zero.
  4. Fail to reject the null: There is enough evidence to conclude the mean is less than zero.
  5. Not enough information given

13. Calculate the mean of the following array: 30 24 59 54 37 48

  1. 40
  2. 42
  3. 50
  4. 38
  5. 65

14. Alpha is also known as:

  1. The power of the test
  2. The significance level of the test
  3. The probability of rejecting a true null
  4. The probability of accepting a false null
  5. B and C

15. If the distribution is symmetric, the mean coincides with:

  1. the test statistic
  2. the standard deviation
  3. the p-value
  4. the median
  5. none of the above

16. The sample mean of exam scores is 91%. The width of the 90% confidence interval is 3%. One of the students claims that the true average is 89%. Using a significance level of 5%, and given what you have learned so far, what should be your response?

  1. Yes, that could be correct.
  2. No, I really think that isn't the true average.
  3. Let me check my magic ball.
  4. I don’t have enough information to comment.
  5. All of the above

17. What criteria do you use when deciding between a Z-test for paired sample means and a t-test for paired sample means?

  1. Whether the sample variances are the same
  2. Whether the mean of the differences is zero or not
  3. Whether the hypothesized mean differences are zero
  4. Whether you know the population standard deviations
  5. Whether the hypothesized mean difference is known

18. If you wish to know if more than 50% of students got question 1 right, what is your null and alternative hypothesis?

  1. H0: p = 0.5 H1: p ≠ 0.5
  2. H0: p > 0.5 H1: p < 0.5
  3. H0: p < 0.5 H1: p > 0.5
  4. H0: p = 0.5 H1: p < 0.5
  5. H0: p = 0.5 H1: p > 0.5

19. Given the following table from excel:

Column1
Mean / 71
Standard Error / 4.94974746
Median / 76.5
Mode / 70
Standard Deviation / 21
Sample Variance / 441
Kurtosis / 3.129032999
Skewness / -1.442696214
Range / 90
Minimum / 10
Maximum / 100
Sum / 1295
Count / 18
Largest(1) / 100
Smallest(1) / 10
Confidence Level(95.0%) / 10.57315878

Which of the following is a reasonable guess for the population mean with a significance level of 5%?

  1. 75
  2. 60
  3. 90
  4. a and b
  5. all of the above

20. What is the test statistic used to test if more than 70% of the population is above 8, given the sample: 1, 10, 34, 15, 8, 40, 90, 41, 5, 16.

  1. –3.16
  2. –1.54
  3. 0.00
  4. 1.54
  5. 3.16

21. The difference between the smallest and largest measurements is:

  1. the average of all measurements
  2. the test statistic as measured in Excel
  3. the range of the measurements
  4. the number of measurements
  5. the difference between the mean and the test statistic

22. A pharmaceutical company currently produces an anesthetic whose effective time is normally distributed with mean 8.2 and standard deviation 2.3. It is considering the launch of a new drug, which they believe has a lower mean effective time but the same standard deviation. In a clinical study meant to test their belief, what would be the appropriate null and alternative hypothesis?

  1. H0: μ ≥ 8.2 H1: μ < 8.2
  2. H0: μ > 8.2 H1: μ ≤ 8.2
  3. H0: μ = 8.2 H1: μ ≠ 8.2
  4. H0: μ ≤ 8.2 H1: μ > 8.2

23. Irrespective of your answer in the last question suppose that you intend to do a two sided test. You collect a sample and compute the sample mean. In order to reject the null hypothesis at a 5% level of significance (the z-value is 1.96, take sample size to be 25),

  1. you need the sample mean to be smaller than 7.298
  2. you need the sample mean to be greater than 9.102
  3. either a or b.
  4. none of the above.

24. The mean of a sample is computed to be –0.301. It has been found out that the p-value is 0.275 when testing Ho: mu = 0 against the two sided alternative H1: mu  0. To test Ho: mu = 0 against the one sided alternative H1:mu<0 at a significance level of 0.40, we will have:

  1. a p-value of 0.275 and therefore reject the null hypothesis
  2. a p-value of 0.138 and therefore reject the null hypothesis
  3. a p-value of 0.862 and therefore accept the null hypothesis
  4. a p-value of 0.5 and therefore the test results will be inconclusive.

25. Which of the following is NOT of the assumptions needed for regression analysis to be valid?

  1. Variance of the error terms must be constant
  2. Error terms must be correlated
  3. Errors must be normally distributed
  4. Error must have a mean of 0
  5. All of the above are necessary for regression analysis to be valid

26. The pooled variance t-test is based on the following assumption(s):

  1. that the two populations be independent
  2. that the two populations have equal variances
  3. that both populations be normal
  4. all of the above.

27. A social scientist is interested in studying levels of police brutality in Des Moines, Iowa and in Verkhyonask, Siberia. She suspects that the police in Des Moines are more brutal. Her data consists of the total number of arrests made in each city every month for one year (so she has 12 observations for each city). Now, arrests don’t necessarily indicate brutality, but ignoring that, what is the correct way to specify this test (let Des Moines be population1):

  1. H0: 1 - 2 = 0 H1: 1 - 2  0
  2. H0: 1 - 2 = 0 H1: 1 - 2 < 0
  3. H0: 1 - 2 = 0 H1: 1 - 2 > 0
  4. H0: 1 - 2 < 0 H1: 1 - 2 > 0

28. For the scenario described above, monthly data the on number of arrests was collected from both cities for a year and a pooled variance t-test was performed at the 5% significance level. The results of the test are presented below.

Des Moines / Verkhyonask
Mean / 57.75 / 55.66667
Variance / 5.840909091 / 13.15152
Observations / 12 / 12
Pooled Variance / 9.496212121
Hypothesized Mean Difference / 0
df / 22
t Stat / 1.655995622
P(T<=t) one-tail / 0.055959227
t Critical one-tail / 1.717144187
P(T<=t) two-tail / 0.111918455
t Critical two-tail / 2.073875294

Based on the correct answer to the last question,

  1. the p-value is 0.056 so we do not reject the null hypothesis
  2. the p-value is 0.112 so we not reject the null hypothesis
  3. the p-value is 0.888 so we do not reject the null hypothesis
  4. the p-value is 0.944 so we do not reject the null hypothesis.

29. The test for difference in proportions between two populations uses

  1. the z-distribution
  2. the f-distribution
  3. the t-distribution
  4. both a and b.

30. With the intention of improving his employees health, the CEO of a Chicago based mutual funds rating company decided to install a rather unique lunch hour exercise program. An hour of undiluted frolic to the peppy rhythmic stylings of the latest Britney Spears Exercise Video should do wonders for employee health was the belief.

Data was collected (in thousands of dollars) during the program’s first year on health-care bills presented to the company, and a test was performed, which compared these numbers with those collected during the year before the exercise program. The results are presented below:

Before / After
Mean / 46.58333 / 43.5
Variance / 277.9015 / 346.6364
Observations / 12 / 12
Pearson Correlation / 0.950326
Hypothesized Mean Difference / 0
Df / 11
t Stat / 1.815066
P(T<=t) one-tail / 0.048424
t Critical one-tail / 1.795884
P(T<=t) two-tail / 0.096847
t Critical two-tail / 2.200986

Based on the given information, which of the following is true?

  1. the average health-care expense was about 46.58 thousand dollars before the exercise program
  2. when performing a one-sided test where the alternative hypothesis states that the program did indeed reduce health-care costs, we can reject the null hypothesis at a 5% level
  3. when performing a two-sided test where the alternative hypothesis states that health-care expenses were different before and after the program, we are NOT able to reject the null hypothesis at the 5% level.
  4. All of the above
  5. None of the above.

31. Suppose you are employed by a lawyer for Richard Simmons who is being sued for running a weight loss scam in California. The claim in the lawsuit is that the weight loss program “Sweating to the Oldies ™” has no effect on people’s weight. You have gathered data on people’s weight both before and after they participated in the program. In order to test whether or not the program had any effect on the participants’ weight, which of the following tests could you run?

  1. paired-sample t-test for difference in means
  2. pooled variance t-test assuming equal variances
  3. pooled variance t-test assuming unequal variances
  4. Z-test for difference in means
  5. F test for difference in variances

32. A local truck manufacturer would like to know if one of the two plants that produce the trucks is more productive than the other (measured by the number of trucks produced per month). Suppose you have gathered data on the number of trucks produced each day for the past year. In order to test whether or not the number of trucks produced by the two plants is different, which of the following tests could be performed?

  1. paired-sample t-test for difference in means
  2. pooled variance t-test assuming equal variances
  3. Z-test for difference in proportions
  4. Z-test for difference in means
  5. F test for difference in variances

33. A local truck manufacturer would like to know whether the percentage of defective trucks is different in the two plants producing trucks. Suppose you have gathered data on the number of defective trucks and the number of total trucks produced at each plant over the last year. In order to test whether there is any difference in the percentage of defective trucks produced in the two plants, which of the following tests could you perform?

  1. paired-sample t-test for difference in means
  2. pooled variance t-test assuming equal variances
  3. Z-test for difference in proportions
  4. Z-test for difference in means
  5. F test for difference in variances

34. A local truck manufacturer would like to know if more than 5% of the trucks produced at a plant are defective. Suppose you have gathered data on the number of defective trucks and the number of total trucks produced over the last year at the plant. In order to test the manufacturer’s claim that more than 5% of the trucks produced are defective, which of the following test could be performed?

a. paired-sample t-test for difference in means

  1. pooled variance t-test assuming equal variances
  2. Z-test for difference in proportions
  3. Z-test for difference in means
  4. Z-test for a single proportion

35. It is often believed that investing in stocks provides a much higher return than investing in bonds, but with higher risk (uncertainty). In order to test whether or not investing in stocks is riskier (returns are more spread out), which of the following tests could be performed?

  1. paired-sample t-test for difference in means
  2. pooled variance t-test assuming equal variances
  3. Z-test for difference in proportions
  4. Z-test for difference in means
  5. F test for difference in variances

Use the following information to answer questions 36-38.

Suppose you believe that the older a person is, the less likely they would be to get in car accidents. You have gathered the following data about the age of five people you know and how many accidents each person has been in during the past year (they are all bad drivers).

AgeAccidents

22 2

21 1

19 6

20 4

187

36. What is the value of the slope coefficient?

  1. –0.577
  2. –1.5
  3. –0.667
  4. 0
  5. 34

37. What is the value of the intercept?

  1. 15.54
  2. -1.5
  3. -20
  4. 34
  5. –26

38. Suppose that the slope of the previous regression model was -1.87. What is the correct interpretation of this coefficient?

  1. An increase in age by 1 year leads to a decrease in estimated average accidents per year by 1.87.
  2. A change in age by 1 year leads to a decrease in estimated average accidents per year by 1.87.
  3. An increase in number of accidents per year by 1 results from an increase in age by 1.87 years.
  4. A decrease in years by 1.87 years leads to an estimated average increase in accidents by 1 per year.
  5. None of the above

Answer Key

1.e25.b

2.b26.d

3.c27.c

4.b28.a

5.e29.a

6.c30.d

7.e31.a

8.a32.b

9.d33.c

10.c34.e

11.d35.e

12.a36.b

13.b37.d

14.e38.a

15.d

16.a

17.d

18.e

19.a

20.c

21.c

22.a

23.c

24.b

Econ173_fa01MidtermAnswersPage 1 of 13