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Please read this first: ▪ This exam contains 9 pages. Please check this. ▪ The exam consists of 20 multiple choice questions and two open questions. ▪ Every multiple choice question has 4 answer alternatives. One of these four is the best alternative, and that is the one you should indicate on the answer form (the red form on your table). Please, follow the instructionson the form on how to use this form. Also fill in on the answer form: the version number of the exam you make, your student number, name, address, the name of the course (BRM), and the date. Do not forget to give your student number both in digits and stripes. ▪ The answers to the open questions can be written in the boxes below each question on the exam itself. ▪ Please write down your name and student number on both the exam (first page + pages with open questions) and the red answer form. ▪ Please show your student card upon request. ▪ If you have finished the exam, please hand in the exam itself and the red form! Grade (with reservation):
( 10 +^ MCQ^ +^ OQ^ ⎞
OQ is the number of points you score on the open questions (max. 45), and MCQ is the number of points you score on the multiple choice questions. MCQ = 45 number of correct answers − 5 15 lOMoAR cPSD| 38783425
RESIT EXAM BUSINESS RESEARCH
METHODS PRE-MSC Questions and
Answers 2024
GOOD
LUCK!
Opgave 1 Multiple Choice Questions
- If P ( A ) = 0.65, P ( B ) = 0.58, and P ( A and B ) = 0.76, then P ( A or B ) is: A. 1. B. 0. C. 0. D. None of these choices
- A mobile phone company distributed a questionnaire among a random sample of their customers. Respondents are asked, among other things, in which of the following age groups they are: 0-25 years; 26-50 years; 51-75 years; 75 years or older. The company wants to test whether the sample distribution by age is equal to that of the Dutch population. Which test is most appropriate? A. Paired Sample T Test B. Kruskal Wallis Test C. Chi-Squared Test D. F-test
- For a 99% confidence interval of the population mean based on a sample of n = 25 with s = 0.05, the critical value of t is: A. 2. B. 2. C. 2. D. 2.
- Three Dutch (national) newspapers (1=Volkskrant, 2=NRC, 3=Telegraaf) asked their readers about their education levels (Low, Medium, High). They want to test whether education level and newspaper are related. Which test is most appropriate? A. Chi-Squared Test B. Independent Samples T Test C. Coefficient of Correlation D. F-test
- For which type of data are the values arbitrary numbers? A. Interval data B. Nominal data C. Ordinal data D. None of these choices
- The sample size needed to estimate a population mean within 2 units with a 95%
- Suppose we wish to test H 0 : = 45 vs. H 1 : 45. What will result if we conclude that the mean is greater than 45 when the actual mean is 50? A. We have made a Type I error B. We have made a Type II error C. We have made both a Type I error and a Type II error D. We have made the correct decision
- A major department store chain is interested in estimating the average amount its credit card customers spent on their first visit to the chain's new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: x = $50.50 and s^2 = 400. A 95% confidence interval for the average amount the credit card customers spent on their first visit to the chain's new store in the mall is: A. $50.50 + $9. B. $50.50 + $10. C. $50.50 + $11. D. None of these choices
- In regression analysis, the coefficient of determination R^2 measures the amount of variation in y that is: A. Caused by the variation in x B. Explained by the variation in x C. Unexplained by the variation in x D. None of these choices
- A regression analysis between sales (in $1,000) and advertising (in $100) resulted in the following least squares line: y ˆ^ = 75 + 6 x. This implies that if advertising is $800, then the predicted amount of sales (in dollars) is: A. $ 4, B. $ 123, C. $ 487, D. $ 12,
- A chi-squared test of a contingency table with 6 degrees of freedom results in a test statistic 2 = 13.58. Using the 2 - tables, the most accurate statement that can be made about the p-value for this test is that: A. p>0. B. p>0. C. 0.05<p<0. D. 0.025<p<0.
- Sample distributions describe the distributions of: A. Population parameters B. Sample statistics C. Both parameters and statistics
D. None of these choices
- An unbiased estimator of a population parameter is defined as: A. An estimator whose expected value is equal to the parameter B. An estimator whose variance is equal to one C. An estimator whose expected value is equal to zero D. An estimator whose variance goes to zero as the sample size goes to infinity
- The width of a confidence interval estimate of the population mean increases when the: A. Level of confidence increases B. Sample size decreases C. Value of the population standard deviation increases D. All of these choices are true
- In a positively skewed distribution: A. The median equals the mean B. The median is less than the mean C. The median is larger than the mean D. The mean can be larger or smaller than the median
- Which of the following is a discrete random variable? A. The Dow Jones Industrial average B. The volume of water in Michigan Lakes C. The time it takes you to drive to school D. The number of employees of a soft drink company
- The probability density function interval [2, 10] is: A. 0. B. 8 C. 6 D. None of these choices f ( x ) for a uniform random variable X defined over the
- Which of the following is not a characteristic for a normal distribution? A. It is symmetrical B. The mean is always zero C. The mean, median, and mode are all equal D. It is a bell-shaped distribution
- A nonparametric test for comparing two populations should be used instead of its parametric counterpart if: A. The sample sizes are large B. The populations have equal means C. The populations are normally distributed
Chi-squared test of a contingency table, because the travel agency wants to test whether a relationship exists between two nominal variables (i.e., reservation method and type of trip). (3 points) 1.5 points for the appropriate test, 1.5 points for the motivation H 0 : The variables trip type (business/leisure) and booking method are independent. H 1 : The two variables are dependent. (3 points) =
P travel agent =
P =
P business (3 points) internet 513 P leisure =
P toll-free number
Question 1 Airline Reservations (20 points)
A travel agency wants to know whether there is an association between the type of trip (business or leisure) and the methods used by customers making airline reservations for their trips. The table below shows the number of air flight reservations by trip type and booking method for a random sample of 513 customers in the target market. Reservation method Business Leisure Used a Travel Agent 256 74 Booked on the Internet 41 42 Airline’s Toll-Free Number 66 34 a. Which test do you consider appropriate for answering this particular research question? Please explain why. b. State the null and alternative hypothesis you want to test. c. Calculate the (estimated) marginal probabilities for each reservation method and trip type. d. Calculate the joint probabilities and the expected frequencies for all possible combinations of trip type and reservation method if we assume the null hypothesis to be true.
The critical 2 - value for α=0.01 and df=(r-1)(c-1)=21=2 is 9.21. (3 points)
( f − e ) 2 i i i = 1 ei
k 70.76 96.
( 42 − 24.27) 2
( 34 − 29.24) 2 = 24.27 29.
The rejection region is 2 (^2) ^ , v = (^2) 0.01,2. Because 2 = 26.81, we reject the null hypothesis and conclude that there is a relationship between reservation method and trip type. (4 points) 2 points for the right answer, 2 points for the interpretation
e. Determine the critical test value for α=0.01 and the appropriate degrees of freedom. f. Is there enough evidence to conclude that there is a relationship between the type of trip (business or leisure) and booking method? Please explain why (not). If we assume the null hypothesis to be true, i.e. the events A and B are independent, then: P ( A & B ) = P ( A ) P ( B ). Hence: P business & travel agent = 0.71 0.64 = 0. P business & internet = 0.71 0.16 = 0. P business & toll-free number = 0.71 0.19 = 0. e business & travel agent = 0.45 513 = 233. e business & internet = 0.11 513 = 58. e business & toll-free number = 0.13 513 = 70. P leisure & travel agent = 0.29 0.64 = 0. P leisure & internet = 0.29 0.16 = 0. P leisure & toll-free number = 0.29 0.19 = 0. e leisure & travel agent = 0.19 513 = 96. e leisure & internet = 0.05 513 = 24. e leisure & toll-free number = 0.06 513 = 29. (4 points) 2 points for the joint probabilities, 2 points for the expected frequencies
A Type I error would occur if we reject a true null hypothesis. (3 points) The probability of a Type I error equals = 0.. (3 points) The differences in salaries between male and female graduates should be normally distributed, if not: Wilcoxon Signed Rank SumTest. The two samples are related, if not: t-test for 1 − 2. The test variable is of interval scale, if not: Wilcoxon Signed Rank SumTest. (4 points) 1 point for each correct assumption and each appropriate test to resolve the issue 1 point as well e. When would we make a Type I error in this case? Please explain in words. f. How large is the probability of a Type I error in this study? g. Which assumptions should be satisfied if you want to use the test you have chosen under c)? Please mention two of them. Also, indicate which test statistic has to be used if the assumptions are not valid? Paired Samples Test Paired Differences Mean Std. Deviation t df Sig. (2-tailed) Std. Error Mean 95% Confidence Interval of the Difference Lower Upper Pair 1 male - female (^) 400.000 434.613 137.437 89.096 710.904 2.910 9. Independent Samples Test Levene's Test for Equality of Variances t-test^ for^ Equality^ of^ Means F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference Lower Upper salary Equal variances assumed .197^ .663^ .547^18 .591^ 400.000^ 730.768^ - 1135.287^ 1935. Equal variances not assumed .547^ 17.715^ .591^ 400.000^ 730.768^ - 1137.062^ 1937. probably caused by reducing the variation between salary offers in each sample. If we use matched pairs we are able to significantly reduce the variance caused by differences in study results between samples, because both samples consists of students who have more or less the same grades. (4 points)
