MT436 – MARKETING RESEARCH METHODS

MT436 – MARKETING RESEARCH METHODS

THIRD EXAMINATION

PART I (25 points): Answer the following on this cover sheet (use back, if necessary. Be sure to clearly indicate your answer to each specific question and show the derivation of your answer where appropriate.

The AU placement office wanted to determine if the average starting salary of marketing graduates is significantly different from that of management grads. In a random sample of 50 recent graduates from each department, the mean starting salary for marketing majors was found to be $24,500 whereas management majors averaged $24, 350. The sample standard deviations were calculated to be $300 and $250 respectively.

a. State the appropriate null and alternate hypotheses.
b. What is calculated test statistic?
c. Assuming that alpha equals .06, can you reject the null? Why or why not?
d. What, specifically, can the placement office conclude from the above?

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PART II (3 points each): Place the letter of the most correct answer in the appropriate place on your scan sheet. Be SURE to indicate the test version in column "J" on your scan sheet.

1. For large samples, use of the normal curve rather than the t distribution typically results in

a. larger confidence intervals.
b. significantly more computations on the part of the researcher.
c. no difference in the width of the confidence intervals.
d. smaller confidence intervals.
e. b and c above.

2. The parametric statistical procedures are appropriate if the data is

a. dependent.
b. metric.
c. nominally scaled.
d. ordinally scaled.
e. none of the above.

3. Which of the following statements about regression/correlation analysis is FALSE?

a. Correlation analysis involves the measurement of the closeness of the relationship between two or more variables.
b. Regression analysis involves the derivation of an equation that, relates the criterion variable to one or more predictor variables.
c. Regression analysis can establish the causal relationship between two or more variables.
d. The least squares equations result from a probabilistic model which relates the variables.
e. The sum of the errors about the regression line in a least squares solution equals zero.

4. The power of a statistical test can be increased by _____sample size, _______the level of significance or using ________tests of significance.

a. decreasing; decreasing; one-tailed
b. increasing; decreasing; one-tailed
c. increasing; reducing; two-tailed
d. decreasing; reducing; two-tailed
e. increasing; increasing; one-tailed

5. A researcher who rejects a null hypothesis when in fact it is true:

a. is committing a Type I error
b. is committing a Type II error
c. is committing neither a Type I nor Type II error
d. is typically sure that he has made an incorrect decision
e. none of the above

6. Which of the assumptions listed below are necessary, in order for the coefficients in a partial regression equation to be interpreted as the average change in the criterion variable associated with a unit change in the appropriate predictor variable holding other predictor variables constant?

a. The predictor variables must be correlated.
b. The variance among predictor variables must be equal.
c. The criterion variable must be normally distributed.
d. The predictor variables must be uncorrelated.
e. None of the above are necessary assumptions.

7. A researcher is interested in analyzing a set of nominal data to determine if the observed pattern of frequencies corresponds to the expected pattern. The appropriate statistical technique is

a. Chi-square contingency table analysis.
b. Kolmogorov-Smirnov test.
c. z-test for one mean.
d. z-test for two means.
e. none of the above.

8. The power of statistical test refers to the probability of ________ and is measured by ______.

a. incorrectly rejecting a true null hypothesis; a
b. correctly accepting a correct null hypothesis; b
c. correctly accepting a correct null hypothesis; 1-b
d. correctly rejecting an incorrect null hypothesis; b
e. correctly rejecting an incorrect null hypothesis; 1-b

9. For the linear equation y = a + b₁X₁, if we do not reject the null hypothesis that b₁ = O₁we may

a. conclude with absolute certainty that no relation exists between X₁ and y.
b. have simply made a Type II error, and thus a relation between x and y may exist.
c. have simply chosen the wrong form of the model to investigate, as the relation between X₁ and y may be nonlinear.
d. conclude that b and c above.
e. conclude that none of the above.

10. The t-test is INAPPROPRIATE for investigating the difference in two sample means when

a. the variance in the two populations can be assumed equal.
b. the characteristic of interest is normally distributed in each population.
c. a pooled estimator for the overall variance is warranted.
d. the data is ordinal or nominally scaled.
e. the samples are independent.

11. If the correlation between two variables x and y is equal to -.90, which of the following is TRUE?

a. x and y are highly related, whereby a positive change in x is accompanied by a positive change in y
b. the two variables x and y are not related to one another
c. x and y are highly related, whereby a negative change in x is accompanied by a positive change in y
d. the coefficient of determination is equal to -.81
e. c and d above

12. In which of the following situations is the calculation of the z-statistic NOT appropriate for making inferences about a single mean?

a. The variable of interest is normally distributed in the population, sigma is known, and n (number of observations) is large.
b. The variable of interest is normally distributed in the population, sigma is known, and n is small.
c. The variable of interest is normally distributed in the population, sigma is unknown, and n is small.
d. The variable of interest is not normally distributed in the population, sigma is known, and n is large.
e. Calculation of the z-statistic is appropriate in each of these situations.

13. Which of the following is true?

a. In most studies the choice of statistical technique by which to analyze the collected data is crucial for proper interpretation of what was found.
b. The conclusion of a study typically does not depend on the statistical method used to analyze the data.
c. With interval scaling it is correct to say that car A had a scale value rating 6 times as great as that of car B.
d. An analyst is interested in determining how the undergraduate grade point averages of students in the Graduate School of
Business and the Law School compare. He should use a statistical test for related samples.
e. All of the above statements are false.

14. A researcher had calculated the sample chi-square test statistic to be equal to X₂ = 7.71. For an alpha level of .10 (i.e., alpha = .10) and 4 degrees of freedom, the critical value of the chi-square statistic is 7.78. The appropriate conclusion is that

a. the sample result is likely to be attributed to chance alone.
b. the null hypothesis should not be rejected.
c. the null hypothesis should be rejected.
d. a and b above are correct.
e. a and c above are correct.

15. Multicollinearity is said to be present in a regression problem if

a. the predictor variables are independent.
b. the criterion variables are independent.
c. the criterion variables are correlated among themselves.
d. the predictor variables are correlated among themselves.
e. the error terms are correlated.

16. In an attempt to minimize error the researcher would like to keep a error as small as possible but he recognizes that an extremely low value of alpha error leads to

a. low b error
b. the need for large samples
c. large opportunity losses
d. indeterminate b errors
e. large b errors

17. The appropriate analysis technique does NOT depend on

a. the power of the test.
b. the type of data.
c. the research design.
d. the assumptions underlying the test statistic.
e. it depends on all of the above.

18. An important philosophical point underlying statistical hypothesis testing is that a null hypothesis may be __________but can never be

a. accepted; rejected
b. incorrectly stated; rejected
c. rejected; accepted
d. unacceptable; rejected
e. rejected; unacceptable

19. A sample of 20 men have been asked to give their opinions on the use of electric razors before and after using a new kind of electric razor. The proper statistical test for examining the data is

a. the t-test of the difference between means.
b. the paired difference test.
c. analysis of variance.
d. regression analysis.
e. none of the above.

20. Compared to the chi-square goodness-of-fit test, when the data are ordinal, the Kolmogorov-Smirnov test is

a. more powerful.
b. easier to compute.
c. does not require minimum cell frequencies for computations.
d. all of the above.
e. a and b only.

21. When we are interested in examining the differences between two groups when a number of characteristics are simultaneously considered, the most appropriate statistical technique is

a. univariate analysis.
b. multiple regression analysis.
c. multivariate test of group differences.
d. t-test for difference in two means.
e. traditional analysis-of-variance procedures.

22. Which linear regression model would be used to represent the relationship between a criterion variable y and a predictor variable having four categories?

a . y = a + b₁X₁
b. y = a + b₁X₁ + b₂X₂
c. y = a + b₁X₁ + b₂X₂ + b₃X₃
d. y = a + b₁X₁ + b₂X₂ + b₃X₃ + b₄X₄
e. none of the above accurately captures the situation

23. The scale skilled, semi-skilled, and unskilled laborer was used to classify respondents in a recent survey. The appropriate measure(s) of central tendency for this variable are

a. the mode.
b. the median.
c. the mode and the median.
d. the mean.
e. the mode, the median, and the mean.

24. An analyst is interested in testing the hypothesis Ho : mu > 15,000. The data consist of 20 observations of an intervally scaled variable which is normally distributed, but with unknown variance. The correct statistical procedure is

a. z-test.
b. t-test.
c. t-test for difference in two means.
d. analysis of variance.
e. chi-square goodness-of-fit test.

25. The percentage of incorrect rejections of the null hypothesis which is expected to occur simply because of random variation in a large number of samples may be referred to as the

a. b risk
b. 1-a risk
c. the confidence level
d. 1-b risk
e. a risk