Question 4 – Undergraduate Degree and MBA Major (3 parts, 14 marks)

The MBA program was experiencing problems scheduling its courses. The demand for the

program’s optional courses and majors was quite variable from one year to the next. In one

year, students seem to want marketing courses; in other years, accounting or finance are the

rage. In desperation, the dean of the business school turned to a Statistics professor for

assistance. The Statistics professor believed that the problem may be the variability in the

academic background of the students and that the undergraduate degree affects the choice

of major. As a start, he took a random sample of last year’s MBA students and recorded the

undergraduate degree and the major selected in the graduate program. The undergraduate

degrees were BA (=1), BEng (=2), BBA (=3), and several others (=4). There are three possible

majors for the MBA students: Accounting (=1), Finance (=2), and Marketing (=3). Can the

Statistics professor conclude that the undergraduate degree affects the choice of major?

a) [2 Marks] Create a cross-classified (or contingency) table with undergraduate degree as

the row and MBA major as the column. The data in this table should be deemed as

observed counts.

b) [3 Marks] Create another table with the corresponding expected counts and having row

totals, column totals, and grand total. Round each cell value to two decimal places.

c) [9 Marks] Perform a chi-square test to assess the association (or independence) between

an undergraduate degree and choice of MBA major at 5% level of significance. Verify the

assumptions required for the chi-square test of independence. Make sure you follow all

the steps for hypothesis testing indicated in the Instructions section and show your

computations.

An SAT prep course claims to improve the test score of students. The table below shows the scores for seven students the first two times they took the verbal SAT. Before taking the SAT for the second time, each student took a course to try to improve his or her verbal SAT scores. Do these results support the claim that the SAT prep course improves the students' verbal SAT scores?

Let d=(verbal SAT scores prior to taking the prep course)−(verbal SAT scores after taking the prep course)d=(verbal SAT scores prior to taking the prep course)−(verbal SAT scores after taking the prep course). Use a significance level of α=0.05 for the test. Assume that the verbal SAT scores are normally distributed for the population of students both before and after taking the SAT prep course.

Student   Score on first SAT   Score on second SAT
1   570   600
2   410   500
3   450   510
4   440   520
5   550   570
6   420   450
7   370   430

Step 1 of 5: State the null and alternative hypotheses for the test.

Step 2 of 5: Find the value of the standard deviation of the paired differences. Round your answer to one decimal place.

Step 3 of 5: Compute the value of the test statistic. Round your answer to three decimal places.

Step 4 of 5: Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to three decimal places.

Step 5 of 5: Make the decision for the hypothesis test.

A psychopharmacologist (a psycholgist interested in the effects of drugs and physiology) is interested in determining the effects of caffeine (from coffee) on performance. Twenty students from a large introductory psychology class volunteered to participate in the study; all were dedicated coffee drinkers and all drank caffeinated coffee. The volunteers were then randomly divided into two groups such that there were ten students in each group. One group of 10 students was asked to study the material while drinking their normal doses of coffee, and to take the exam while drinking their normal doses of coffee before the test. This group is called the “Coffee with Test” group.

The second group of 10 students was asked to study the exam material while drinking their normal doses of coffee, but to take the without having consumed coffee for at the least 3 hours beforehand. This group is called the “No-Coffee with Test” group. One student from the “No-Coffee with Test” group became ill and was unable to sit for the. The researcher recorded the number of correct responses on the . The scores are below.

With  = .01, complete step 4 of the hypothesis testing procedure, what decision and conclusion should the researcher make?

The researcher should reject H₀ and conclude that there is a difference in performance with no caffiene versus caffiene.

The researcher should retain H₀ and conclude that caffeine has no effect on performance

The researcher should reject H_A and conclude that caffeine affects performance

The researcher should reject H₀ and conclude that caffeine has no effect on performance

No answer text provided.

Administrators want to know if test anxiety is impacted by the number of college years completed. After completing their freshman year, a random sample of students was selected and given the College Test Anxiety Questionnaire (CTAQ); higher scores indicate more test anxiety. After completing their junior year they were again tested. What can the administrators conclude with α = 0.05?

a) What is the appropriate test statistic?
---Select---naz-testOne-Sample t-testIndependent-Samples t-testRelated-Samples t-test

b)
Condition 1:
---Select---CTAQnumber of college yearsfreshmanjuniortest anxiety
Condition 2:
---Select---CTAQnumber of college yearsfreshmanjuniortest anxiety

c) Input the appropriate value(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
p-value = _______; Decision: ---Select---Reject H0Fail to reject H0

d) Using the SPSS results, compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
d = ______; ---Select---natrivial effectsmall effectmedium effectlarge effect
r² =________ ; ---Select---natrivial effectsmall effectmedium effectlarge effect

e) Make an interpretation based on the results.

Students showed significantly less anxiety in their junior year as opposed to their freshman year.

Students showed significantly more anxiety in their junior year as opposed to their freshman year.

    Students showed no significant anxiety difference between their junior and freshman year.

1.

A three-digit number is formed from nine numbers (1, 2, 3, 4, 5, 6, 7, 8 & 9). No number can be repeated. How many different three-digit numbers are possible if 1 and 2 will not be chosen together?

Select one:

A. 672

B. 210

C. 462

D. 336

2.

In a recent survey conducted by a professor of UM, 200 students were asked whether or not they have a satisfying experience with the e-learning approach adopted by the school in the current semester. Among the 200 students interviewed, 121 said they have a satisfying experience. What is the 99% confidence interval for the proportion of all UM students who have a satisfying experience with the e-learning approach?

Select one:

A. 0.537 to 0.673

B. 0.548 to 0.662

C. 0.516 to 0.694

D. 0.524 to 0.686

3.

Suppose a professor wants to estimate the proportion of UM students who have a satisfying experience with the e-learning approach adopted by the school in the current semester. What is the minimum sample size that he should use if he wants the estimate to be accurate within 0.06 with a 90% confidence?

Select one:

A. 188

B. 267

C. 456

D. 752

4.

According to a poll on customer behavior, 30% of people say they will only consider cars manufactured in their country when purchasing a new car. Suppose you select a random sample of 180 respondents. The probability is 80% that the sample percentage will be contained within what symmetrical limits of the population percentage?

Select one:

A. 25.6% and 34.4%

B. 27.1% and 32.9%

C. 24.4% and 35.6%

D. 23.3% and 36.7%

There is some evidence that high school students justify cheating in class on the basis of poor teacher skills. Poor teachers are thought not to know or care whether students cheat, so cheating in their classes is OK. Good teachers, on the other hand, do care and are alert to cheating, so students tend not to cheat in their classes. A researcher selects three teachers that vary in their teaching performance (Poor, Average, and Good). 6 students are selected from the classes of each of these teachers and are asked to rate the acceptability of cheating in class.

How acceptable is cheating in class?

Extremely Very Somewhat Neutral Somewhat Very Extremely unacceptable unacceptable unacceptable acceptable acceptable   acceptable 1 2 3 4 5 6 7

a. Use SPSS to conduct a One-Way ANOVA with α= 0.05 to determine if teacher quality has a significant effect on cheating acceptability. State your hypotheses, report all relevant statistics, include the ANOVA table from SPSS, and state your conclusion.

b. Use SPSS to conduct post hoc testing. To run a post hoc test in SPSS, open the One-Way ANOVA window (used above) and click the “Post Hoc” button. Check the boxes next to LSD and Bonferroni.

State the results of the post hoc tests (which means are significantly different from each other) and include SPSS printouts as part of your answer to this question.

A researcher believes that college students today have different IQ scores than in previous years. To investigate this belief, he randomly samples 41 currently enrolled students and records their IQ scores. The scores have a mean of 111 and a standard deviation of 12.4. A local census taken 10 years ago shows that the mean IQ of students enrolled during that time was 115.

The degrees of freedom for this sample is                            [ Select ]                       ["41", "40", "39", "38", "-2.201", "-2.407", "2.704", "2.021", "-2.07", "+2.07", "-0.32", "+0.32", "reject the null hypothesis", "fail to reject the null hypothesis", "IQ is probably different", "IQ is not different"]         

Using a two tailed alpha level of .01, the appropriate critical value is                             [ Select ]                       ["41", "40", "39", "38", "-2.201", "-2.407", "2.704", "2.021", "-2.07", "+2.07", "-0.32", "+0.32", "reject the null hypothesis", "fail to reject the null hypothesis", "IQ is probably different", "IQ is not different"]         

The obtained value of the appropriate statistic is                            [ Select ]                       ["41", "40", "39", "38", "-2.201", "-2.407", "2.704", "2.021", "-2.07", "+2.07", "-0.32", "+0.32", "reject the null hypothesis", "fail to reject the null hypothesis", "IQ is probably different", "IQ is not different"]         

What is your decision?                             [ Select ]                       ["41", "40", "39", "38", "-2.201", "-2.407", "2.704", "2.021", "-2.07", "+2.07", "-0.32", "+0.32", "reject the null hypothesis", "fail to reject the null hypothesis", "IQ is probably different", "IQ is not different"]         

Is the IQ of currently enrolled college students different than in previous years?                            [ Select ]                       ["41", "40", "39", "38", "-2.201", "-2.407", "2.704", "2.021", "-2.07", "+2.07", "-0.32", "+0.32", "reject the null hypothesis", "fail to reject the null hypothesis", "IQ is probably different", "IQ is not different"]         

The Gourmand Cooking School runs short cooking courses at its small campus. Management has identified two cost drivers that it uses in its budgeting and performance reports—the number of courses and the total number of students. For example, the school might run two courses in a month and have a total of 63 students enrolled in those two courses. Data concerning the company’s cost formulas appear below:

Fixed Cost per Month Cost per Course Cost per
Student
Instructor wages $ 2,980
Classroom supplies    $ 300
Utilities $ 1,210 $ 85
Campus rent $ 5,000
Insurance $ 2,300    
Administrative expenses $ 3,900 $ 41 $ 4

For example, administrative expenses should be $3,900 per month plus $41 per course plus $4 per student. The company’s sales should average $850 per student.

The actual operating results for September appear below:

Actual
Revenue $ 50,650
Instructor wages $ 11,200
Classroom supplies $ 18,750
Utilities $ 1,960
Campus rent $ 5,000
Insurance $ 2,440
Administrative expenses $ 3,742

Required:

1. The Gourmand Cooking School expects to run four courses with a total of 63 students in September. Complete the company’s planning budget for this level of activity.

2. The school actually ran four courses with a total of 59 students in September. Complete the company’s flexible budget for this level of activity.

3. Complete the flexible budget performance report that shows both revenue and spending variances and activity variances for September. (Indicate the effect of each variance by selecting "F" for favorable, "U" for unfavorable, and "None" for no effect (i.e., zero variance). Input all amounts as positive values.)