ΘΕΜΑΤΑ ΕΞΕΤΑΣΕΩΝ 2008/9
HELLENIC OPEN UNIVERSITY: MBA PROGRAM
MBA60: Advanced Quantitative Methods for Managers
Summer 2009 Examination
Question 1 (2 Marks)
Twenty multiple-choice questions follow. For each question circle the correct answer.
1. Which of the following is true for a normal distribution?
a. P(x>8) = P(x≥9) c. P(x<5) ≠P(x≤5)
b. P(2<x≤8) = P(2≤x<8) d. P(x≤8) = P(x≤8.5)
2. The standard error of the mean of a sample of 100 items from a population will be equal to _________ the standard error of the mean of a sample of 25 items.
a. ¼ times c. 4 times
b. ½ times d. 2 times
3. The sample mean will probably be closer to the population mean if:
a. the population standard error is large c. the sample standard error is small
b. the population size is large d. the sample size is small
4. If we want to change a standard error from 12 to 4 by changing the sample size, we need to multiply the original sample size by:
a. 3 c. 1/3
b. 9 d. 1/9
5. In a large-sample hypothesis test with an alternative hypothesis of mean>60, the p-value equals to:
a. a c. the critical value of z
b. b d. the area to the right of the obtained z
6. A null hypothesis (H0) will be rejected if:
a. a = .05 and p-value = .15 c. a = .01 and p-value = .03
b. a = .05 and p-value = .03 d. obtained z close to the (H0) mean
7. The hypothesis that two population standard deviations are equal can be rejected at the 5% significance level if:
a. F>F(.10) c. F>F(.20)
b. F>F(.05) d. F<F(.05)
8. A placement office at a large university claims that approximately 70% of the school’s accounting graduates will obtain jobs in their field upon graduation. The accounting department feels that the percentage is larger than 70%. From a random sample of 100 recently graduated accounting majors, it was found that 75 had obtained jobs in their field. The hypotheses are:
a. H0: p1-p2 = .70, H1: p1-p2 > .70 c. H0: p < .70, H1: p ≥ .70
b. H0: p = .70, H1: p > .70 d. H0: p = .70, H1: p ≠ .70
9. In a study to determine if a student’s junior year electives in college are independent of his or her major, a sample of 200 students was found to contain 40 juniors with accounting as one of the electives, and 50 with major in accounting. If the null hypothesis of independence is true, the expected frequency of students who both as juniors and as majors selected accounting is:
a. 10 c. 25
b. 20 d. 15
10. In regression analysis the normal equations are obtained from minimizing:
a.
Σ(
y – ŷ)²
c.
Σ(
y – ŷ)
b.
Σ(
y –
)²
d.
Σ(
– ŷ)
11. Which of the following pairs of statements cannot both be true?
a. ŷ = 5 - 5x and r = .20 c. ŷ = -6 - 8x and r = -.40
b. ŷ = 8 + 2x and r = . 40 d. ŷ = -9 + 10x and r = .60
12. If in a correlation analysis, the hypothesis that ρ = 0 is rejected, then:
a. s must be zero c. the regression slope = 0
b. r² must be close to 1 d. there is a relationship between x and y
13. The coefficient of determination is equal to:
a. total variation c. one minus the proportion of
unexplained variation
b. the unexplained variation d. the square root of the
explained variation
14. If a perfect curvilinear relationship exists between two variables, but no linear relationship exists, then:
a. r = 1 c. r = ±1
b. r = 0 d. r is meaningless.
15. The sum Σ(ŷ -
)² is called the _________ sum of squares. a. regression c. least
b. total d. residual
16. The sum Σ(y-)² is called the _________ sum of squares. a. regression c. least
b. total d. residual
17. The symbol used to indicate the y values of points on a least-squares line is:
a. b c. ŷ
b. ỹ d. y
18. A small computed X² value for a contingency table, which of the following concerning the two variables, reveals?
a. a strong relation between them c. the observed frequencies differ
from the expected frequencies
b. one is dependent on the other d. one is independent of the other
19. In conducting a hypothesis test, the procedure always assumes that:
a. H1 is true c. H0 is true
b. H1 is false d. H0 is false
20. When a null hypothesis cannot be rejected, we conclude that:
a. H0 is true c. H1 is true
b. H0 may be true d. H1 may be true.
Question 2 (3 Marks)
In a study to evaluate the time required to turn around its airplanes, an airline company has randomly sampled 50 airplane records. The turnaround times, measured in minutes, for the sampled planes are as follows:
| 51 | 52 | 54 | 59 | 61 | 62 | 64 | 65 | 66 | 68 |
| 69 | 71 | 73 | 74 | 74 | 75 | 77 | 77 | 78 | 79 |
| 81 | 81 | 82 | 84 | 85 | 86 | 87 | 87 | 88 | 88 |
| 88 | 89 | 89 | 90 | 91 | 93 | 94 | 95 | 96 | 96 |
| 97 | 99 | 101 | 103 | 104 | 106 | 108 | 111 | 114 | 118 |
2. Classify the above data in a suitable frequency distribution; construct the histogram and comment on its main characteristics.
3. On the basis of the above results, if you had to tell the operations manager of the airline company how long a plane should expect to wait to be turned around, what would you say? Explain.
Let the variable X represents the average grade of a randomly selected student from a university. It is known that the distribution of X has a mean of 2.5 and a standard deviation of 0.6. If a random sample of n = 36 students is taken and the value of 
is calculated, what is the probability that will
1. Be less than 2.4
2. Be in the interval (2.4 - 2.7)
3. Assuming that the standard deviation of X is not known, and a sample of 100 students yielded the sample values = 3.3 and s = 0.9. What is a 95% confidence interval for the university average grade based on these sample values?
4. Assuming that the standard deviation of X is not known, another sample of n = 16 students yielded the sample values = 2.7 and s = 0.6. What is a 95% confidence interval for the university average grade based on these sample values?
(Note: Two-tail Z and t-values for 95% confidence interval: Z = 1.96, t14 = 2.145, t15 = 2.131, t16 = 2.120)
Question 4 (3 Marks)
The European Competition Commission investigates whether the pharmaceutical industry practices international price discrimination. For this purpose the Commission formulates a model of the prices of pharmaceuticals using cross section data of 32 European countries. The variables used are the following:
(Dependent variable) pharmaceutical price index in the ith country (average for all European countries = 100)
The per capita domestic product in the ith country (000 €)
The per capita volume index of consumption of pharmaceuticals in the ith country (average for all European countries = 100)
Dummy variable = 1 if patents of pharmaceutical products are recognized in the ith country
= 0 otherwise
Dummy variable = 1 if the ith country applies strict price control = 0 otherwise.
Dummy variable = 1 if the ith country encourages price competition= 0 otherwise.
The relevant model has been estimated using OLS and the results ate presented below:
Model Summary
Model | R | R Square | Adjusted R Square | Standard Error |
|
| 0.900 | 0.811 | 0.775 | 16.490 |
Coefficients
|
| Coefficients |
t | Significance (P-value) |
| b | Std. Error |
| Constant | 38.220 | 6.387 | 5.984 | 0.000 |
| GDP | 1.434 | 0.214 | 6.687 | 0.000 |
| CP | -0.595 | 0.224 | -2.656 | 0.013 |
| PP (dummy) | 7.311 | 6.123 | 1.194 | 0.243 |
| PC (dummy) | -15.629 | 6.933 | -2.254 | 0.033 |
| PCM (dummy) | -11.385 | 7.159 | -1.590 | 0.124 |
1. State the estimated regression equation.
2. Comment on the significance of the regression coefficients.
3. Give the interpretation of the significant regression coefficients.
4. Interpret the coefficient of determination.
5. Do you think that international price discrimination exists? Provide the proper explanation.
