MGMT2263 final exam practice questions
This covers material since the midterm. Of course, you should be able to solve problems from before the midterm.
Question 1
An office supply store examined annual expenditures on office supplies for a sample of its customers, segregating them by number of employees. These were the results:
|
Under 10 |
10 to 49 |
50 to 99 |
100+ |
|
50 |
85 |
120 |
102 |
|
125 |
92 |
105 |
125 |
|
80 |
65 |
114 |
134 |
|
72 |
110 |
95 |
105 |
|
65 |
100 |
120 |
122 |
|
75 |
102 |
117 |
140 |
|
85 |
98 |
102 |
117 |
|
95 |
102 |
135 |
128 |
Analysis of the data indicates it is normally distributed.
a) Is there any significant difference in average annual expenditures among the companies of different sizes? Test at a 5% level of significance.
b) Estimate the p-value. Interpret the p-value.
c) For which size companies is there a significant difference? Test at a 5% level of significance.
d) Construct a 95% confidence interval of the difference between the groups with the largest and smallest averages. Why is this confidence interval consistent with the results of the analysis in part a?
Question 2
Four special-ed classes were taught math using different pedagogies. These were the results of the final exam:
|
Class 1 |
Class 2 |
Class 3 |
Class 4 |
|
52 |
62 |
24 |
8 |
|
60 |
70 |
80 |
92 |
|
29 |
71 |
82 |
12 |
|
84 |
72 |
39 |
15 |
|
43 |
18 |
85 |
87 |
|
33 |
65 |
32 |
80 |
|
40 |
65 |
39 |
16 |
|
51 |
69 |
41 |
85 |
Analysis of the data indicates that not all the class data are normally distributed. (Classes 3 and 4 in particular appear to be bimodal.)
a) Is there any significant difference in the pedagogies? Test at a 5% level of significance.
b) Suppose a level of significance had not been chosen. Why would the same conclusion be reached?
Question 3
A sales office wanted to examine the relationship between the number of hours per week its sales staff cold-called and gross monthly income. These are the results (income in thousands of dollars):
|
hours |
12 |
15 |
10 |
20 |
14 |
30 |
16 |
22 |
8 |
17 |
|
income |
6.2 |
6.8 |
4.5 |
9.2 |
6.6 |
12.2 |
7.4 |
10.3 |
4.8 |
8.9 |
a) Calculate Sxx, Syy and Sxy.
b) If the number of hours cold-calling is used to predict monthly gross income, manually calculate the slope and intercept and state the model. Round the values to 4 decimals.
c) Manually calculate the correlation coefficient. What does it mean in the context of this problem?
d) What percentage of the variation in income is explained by the number of hours cold-calling?
e) Is the model significant? Test at a 5% level of significance.
f) Suppose instead that we want to determine if there is a significant positive relationship between hours and income. Test at a 5% level of significance.
g) Construct a 95% confidence interval of the slope. If this confidence interval were used to test the hypothesis in part c, why would the same conclusion be reached?
h) If a person cold-calls 25 hours per week, what would be the expected gross monthly income? Round to the nearest dollar.
i) Construct a 95% confidence interval of the average gross monthly income based on 25 hours of cold calling per week.
Question 4
Three judges were asked to rate 6 pairs of dancers. These were the results:
|
|
Judge 1 |
Judge 2 |
Judge 3 |
|
Pair 1 |
5 |
6 |
6 |
|
Pair 2 |
10 |
9 |
9 |
|
Pair 3 |
7 |
5 |
5 |
|
Pair 4 |
1 |
1 |
3 |
|
Pair 5 |
8 |
8 |
8 |
|
Pair 6 |
7 |
8 |
8 |
a) Is there any significant difference among the judges in how they rated the pairs? Test at a 5% level of significance.
b) Is there any significant difference among the couples in how they are rated? Test at a 5% level of significance.
c) For the test in part b, in what range does the p-value fall?
Question 5
A company with 4 offices examined the monthly expenses in a variety of categories. These were the results (in thousands of dollars):
|
|
Office 1 |
Office 2 |
Office 3 |
Office 4 |
|
Salary |
50.2 |
46.3 |
60.7 |
52.3 |
|
Utilities |
1.3 |
1.4 |
0.9 |
1.5 |
|
Office
supplies |
0.7 |
0.6 |
1.3 |
0.9 |
|
Transportation |
1.2 |
0.8 |
1.5 |
0.9 |
|
Entertainment |
0.5 |
0.4 |
0.6 |
0.5 |
|
Miscellaneous |
2.3 |
1.8 |
1.7 |
1.9 |
Analysis of the data in each category indicates it is normally distributed.
a) Is there any significant difference among the offices in their average monthly expenses? Test at a 5% level of significance.
b) If salary is excluded, is there any significant difference among the expense categories? Test at a 5% level of significance.
c) Between which expense categories is there a significant difference at a 5% level of significance?
Question 6
A researcher examined the relationship between gross annual income and number of employees. These were the results:
|
|
< 10 |
10 to 19 |
20 to 49 |
50 + |
Total |
|
< $10K |
286 |
300 |
142 |
5 |
733 |
|
$10K to
under $25K |
42 |
152 |
130 |
29 |
353 |
|
$25K to
under $50K |
7 |
62 |
25 |
56 |
150 |
|
$50K + |
0 |
9 |
8 |
89 |
106 |
|
Total |
335 |
523 |
305 |
179 |
1342 |
a) If we test to see if gross annual income depends on the number of employees at a 5% level of significance, show why the first term of the test statistic (using the observed value of 286) is sufficient to reject the null hypothesis.
b) To what degree does gross annual income depend on the number of employees? Round to 2 decimals.
Question 7
A real estate firm wanted to see which of square footage (reported in hundreds), number of bedrooms, whether the house has an attached garage or not (attached=1) and whether the house has a developed basement or not (developed=1) contributes to the selling price of a house (reported in thousands). The initial model using all the variables had the following results:
|
SUMMARY
OUTPUT |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Regression Statistics |
|
|
|
|
|
|
|
|
Multiple
R |
0.9456 |
|
|
|
|
|
|
|
R Square |
0.8942 |
|
|
|
|
|
|
|
Adjusted
R Square |
0.8338 |
|
|
|
|
|
|
|
Standard
Error |
36.1073 |
|
|
|
|
|
|
|
Observations |
12 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
ANOVA |
|
|
|
|
|
|
|
|
|
df |
SS |
MS |
F |
Significance F |
|
|
|
Regression |
4 |
77145.6604 |
19286.4151 |
14.7932 |
0.0016 |
|
|
|
Residual |
7 |
9126.1687 |
1303.7384 |
|
|
|
|
|
Total |
11 |
86271.8292 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
VIF |
|
Intercept |
-11.0880 |
76.5998 |
-0.1448 |
0.8890 |
-192.2176 |
170.0415 |
|
|
sq. ft. |
21.5768 |
4.5930 |
4.6978 |
0.0022 |
10.7161 |
32.4376 |
2.5561 |
|
bedrooms |
33.3956 |
13.0367 |
2.5617 |
0.0375 |
2.5687 |
64.2226 |
1.3362 |
|
garage |
-30.7437 |
36.9822 |
-0.8313 |
0.4332 |
-118.1927 |
56.7053 |
2.7975 |
|
basement |
38.9510 |
27.0114 |
1.4420 |
0.1925 |
-24.9207 |
102.8227 |
1.6323 |
a) If a house has 1500 square feet, 3 bedrooms, an attached garage and an undeveloped basement, what would be the average selling price? Round to the nearest thousand.
b) You will note that the coefficient for basement is positive and that its p-value is 0.1925. If we wanted to determine if there is a significant positive relationship between having a developed basement and selling price, what would be the conclusion if a level of significance were not specified?
c) Construct a 95% confidence interval of the coefficient for square footage.
Two more models were built:
|
SUMMARY
OUTPUT |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Regression Statistics |
|
|
|
|
|
|
|
|
Multiple
R |
0.9276 |
|
|
|
|
|
|