Department of marketing

Statistics Examination for marketing

Name___________________________________ID.N O__________ Time Allowed:
INSTRUCTIONS

 Please fill in your Name and Id. No on top of every answer sheet.
 ALL questions should be attempted and use of scientific calculator is allowed.
 The tables are attached at the end of the exam paper.
 Please use a Black or Blue pen to answer the questions
 Show all your works to earn full marks and illegible answers will have no credit.

Part I: Choose the correct answer among the given alternatives (2pts each)
1. If the regression equation is equal to y=23.6−54.2x, then 23.6 is the _____ while -54.2 is the ____ of
the regression line. . A. Slope, intercept B. Slope, regression coefficient C. Intercept, slope D.
Radius, intercept.
2. To address whether two variables are related in a contingency table, the null hypothesis, H o says that:
A. The two variables are independent. B. The two variables are dependent.
C. The two variables are equal. D. None of these choices
3. Which statistical technique is appropriate when we wish to analyze the relationship between two
qualitative variables with two or more categories?
A. The chi-squared test of a multinomial experiment. C. The chi-squared test of a contingency table.
B. The t-test of the difference between two means. D. The z test of the difference between two
proportions.
4. Which of the following is true of the null and alternative hypotheses?
A. Exactly one hypothesis must be true C. both hypotheses must be true
B. It is possible for both hypotheses to be true D. It is possible for neither hypothesis to be true
5. The degrees of freedom for the Chi-Square test statistic when testing for independence in a contingency
table with 3 rows and 5 columns would be: A. 5 B. 10 C. 8 D. 9
6. In the past, the mean running time for a certain type of flashlight battery has been 30 hours. The
manufacturer has introduced a change in the production method and wants to perform a hypothesis test
to determine whether the mean running time has changed as a result.
A. H0: µ ≠30 hours Vs H1: µ =130 hours C. H0: µ =30 hours Vs H1:µ ≠30 hours
B. H0: µ =30 hours Vs H1: µ >30 hours D. H0: µ ≥130 hours Vs H1:µ =30 hours
7. In hypothesis testing, type II error occurs when
A. The null hypothesis is not rejected when the null hypothesis is true.
1|Page
 B. The null hypothesis is rejected when the null hypothesis is true.
C. The null hypothesis is not rejected when the null hypothesis is false.
D. The null hypothesis is rejected when the alternative hypothesis is true.
8. Which of the following would be an appropriate null hypothesis?
A. The mean of a population is equal to 50. B. The mean of a sample is equal to 50.
C. The mean of a population is greater than 50. D. Only (a) and (c) are true.
9. The correlation coefficient is used to determine:
A. specific value of the y-variable given a specific value of the x-variable
B. specific value of the x-variable given a specific value of the y-variable
C. The strength of the relationship between the x and y variables
D. None of these
10. In the simple linear regression equation, the symbol x represents the
A. Estimated or predicted response B. Estimated intercept C. Estimated slope D. Independent
variable
11. A regression between foot length (Dependent variable in cm) and height (independent variable in
inches) for 33 students resulted in the following regression equation: yˆ = 10.9 + 0.23 x. One student in
the sample was 73 inches tall with a foot length of 29 cm. What is the predicted foot length for this
student? A. 17.57 cm B. 27.69 cm D. 29 cm C. 33 cm

12. Describe the type of association shown in the following scatterplot:

A. Positive linear association

B. Negative linear association
C. Positive curvilinear association
D. Negative curvilinear association
13. If the slope of the regression equation y = bo + b1x is positive, then;
A. as x increases y decreases
B. as x increases so does y

2|Page
 C. Either a or b is correct
D. as x decreases y increases
14. The correlation coefficient is used to determine:
A. specific value of the y-variable given a specific value of the x-variable
B. specific value of the x-variable given a specific value of the y-variable
C. The strength of the relationship between the x and y variables
D. None of these
15. If there is a very strong correlation between two variables then the correlation coefficient must be
A. any value larger than 1
B. much smaller than 0, if the correlation is negative
C. much larger than 0, regardless of whether the correlation is negative or positive
D. None of these alternatives is correct.
16. Contingency tables and degrees of freedom are key elements of the chi-square test
A. True B. False
17. If α =5%, the Z-value of one-tailed test will be: A 1.645 B.2.58 C. 1.96 D. 2.33
18. Analysis of variance is a statistical method of comparing the ________ of several populations.
A) variances B) means C) proportions D) standard deviations E) none
19. In a one-way ANOVA, the independent variable comprises two levels (k=2). If SSB = 20 and MSE =
4, the F-statistic for testing the null hypothesis would equal to_________.
A) 0.2 B) 2 C) 5 D) 10 E) 40
20. A fisheries researcher wishes to test for a difference in mean weights of a single species of fish caught
by fishermen in three different lakes in Ethiopia. The significance level for the test will be 0.05. use the
given information to answer questions 23 to 25
SSB=17.04, TSS=31.23, SSW=14.19 n=12
The null hypothesis for this analysis is:
A. Not all the fish populations have the same mean.
B. At least one of the fish populations has a different mean.
C. μ1 = μ2 = μ3 D. μ1 = μ2 = μ3 = 0 E. None of these.
21. The value of Fstatistic for this test is: A. 8.52 B. 5.39 C. 2.00 D. 0.1854
22. The value of FCRIT/tabulated for this test is: A. 3.5874 B. 3.8625 C. 3.9824 D. 4.2565
23. Which of the following number cannot be probability?
A. 1/4 B. ½ C. 3/2 D. all
24. Set of all possible outcomes of a probability experiment
3|Page
 A. Event B. Sample space C. Random experiment D. complementary event
25. What is the listing of all possible outcomes of an experiment and their corresponding probability of
occurrence called?
A. Probability Distribution B. Frequency Distribution C. Random Variables E. None
26. In how many ways can 2 players be selected from a group of 5 players?
A. 20 B. 6 C. 10 D. 120
27. A random variable X has a mean of 15 and E ( X 2 ) = 289. The standard deviation of X is:
A. 8 B. 5 C. 9 D. 10
28. 15% of the students registered in the 1 st semester join the Management department. If 100 students are
registered, how many of them are expected to join the Management department
A. 15 B. 5 C. 25 D. 75
29. Which one of the following random variables is continuous probability distribution?
A. Poisson B. Hyper geometric C. Normal D. Binomial
30. The variance of a sample of 25 observations equals 36. The standard deviation of the sample equals
A. 5 B. 6 C. 8 D. 9
31. The letters in the word “STATISTICS” arranged in ________________different ways.
A. 12000 B. 50400 C. 20000 D. 84000
32. The probability that a regularly scheduled flight departs on time is P(D)=0.83; the probability that it
arrives on time is P(A)=0.82; and the probability that it departs and arrives on time is P(D∩A) =0.78.
Find the probability that a plane arrives on time, given that it departed on time
A. 0.94 B. 0.84 C. 0.95 D. 0.65
33. Normal distribution is symmetric about: A. Mean B. Median C. Mode D. All the above
34. The mean of standard normal distribution is ___ and standard deviation is ___.
A. 1, 0 B. 1, 1 C. 0, -1 D. 0, 1
35. Two events A and B are ________ if the occurrence (or non-occurrence) of one event has an effect on
the probability of the occurrence (or non-occurrence) of the other event.
A. Statistically independent B. Mutually exclusive C. Statistically dependent D. None
36. What is the listing of all possible outcomes of an experiment and their corresponding probability of
occurrence called? A. Probability Distribution B. Frequency Distribution C. Random Variables D.
None
37. If you have a data set that consists of the following three values 1, 2, and 3, which of the following
statements are true:

4|Page
 A. The range of the data is 3. B. The sample standard deviation equals the sample average. C. The
sample standard deviation equals the sample variance. D. Both (A) and (B) are true.
38. The coefficient of variation for a set of annual incomes is 20%; the coefficient of variation for the
length of service with the company is 39%. What does this indicate?
A. More dispersion in the distribution of the incomes compared with the dispersion of their
length of service
B. More dispersion in the lengths of service compared with income
C. Dispersion in the two distributions (income and service) cannot be compared
D. Dispersions are equal
39. A manager models project completion times as normally distributed with a mean of 20 days and
standard deviation of 5 days. What is the probability a project finishes in less than 15 days?
A. 0.1587 B. 0.3400 C. 0.5000 D. 0.8400
40. While conducting a field survey in a remote area, a geologist needs to collect soil samples. Due to time
constraints, they decide to take samples from locations that are easiest to access. What sampling
method is this? A. Random sampling B. Systematic sampling C. Convenience sampling D.
Cluster sampling
41. In which distribution, the probability success remains constant from trial to trial?
A. Hypergeometric B. Binomial C. Normal D. Poisson

42. The total area the normal curve is: A. 0.5 B. 1.0 C. 0.6 D. 0.9
43. What is the variance of a binomial distribution with n=10 and p=0.5?
A. 2.5 B. 5.0 C. 10.0 D. 25.0

44. If two events A and B are mutually exclusive, what is P(A B)?
A. 1 B. 0.5 C. 0 D. 0.2

45. The mean of an examination is 69, the median is 68, the mode is 67, and the standard deviation is 3.
The measures of variation for this examination is:
A. 67 B. 68 C. 69 D. 3

46. The ratio of the standard deviation to the arithmetic mean expressed as a percentage is called:
A. Coefficient of standard deviation

B. Coefficient of skewness

C. Coefficient of kurtosis

D. Coefficient of variation

5|Page
47. An electrical firm manufactures light bulbs that have a life, before burn-out, that is normally distributed
with mean equal to 800 hours and a standard deviation of 40 hours. Find the probability that a bulb
burns between 778 and 834 hour?

A. 0.5111 B. 0.2912 C. 0.8023 D. 0.2329

48. A bank categorizes loan applicants as either high-risk or low-risk:12% of applicants are high-risk
borrowers; 30% of high-risk borrowers default on loans; 6% of low-risk borrowers default on loans. If
a borrower defaults, what is the probability that they were high-risk?

A. 0.2821 B. 0.0132 C. 0.0038 D. 0.4054

49. In quality control, a factory produces bolts with a mean length of 5 cm and standard deviation of 0.2
cm. What is the z-score for a bolt measuring 5.6 cm?

A. 3.0 B. 2.0 C. 1.0 D. 0.6

50. Which of the following is a discrete probability distribution?

A. P(0) = 0, P(1) = 1/4, P(2) = 3/4

B. P(0) = 1/4, P(1) = 1/2, P(2) = 3/4
C. P(0) = 1/10, P(1) = 1/5, P(2) = 1/4
D. P(0) = 1/8, P(1) = 1/8, P(2) = 1/8

6|Page
7
8