BUS 226 Final Exam(96 points)
Please answer each question there is no penalty for guessing. Point values are noted for each question. The exam is open-book and open notes. Calculators and computers are allowed.
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1. (2 points). (False) The median is very sensitive to extreme data points.
2. (2 points). (True ) The t-distribution approaches the standard normal distribution as sample size increases.
What type of data (attribute, discrete numerical, continuous numerical) is each of the following variables:
3. (2 points) ___________attribute__________ Your gender
4. (2 points) _________discrete numerical____________ Your height
Which type of data (nominal, ordinal, interval, ratio) is each of the following variables?
5. (2 points) __________interval___________ Temperature in degrees Fahrenheit
6. (2 points) ___________ratio__________ Your weight
7. (3 points). 500 names are selected from a list containing 1,000 people by choosing every other name. Which sampling method is this?
A) Simple random sample.
B) Systematic sample.
C) Stratified sample.
D) Cluster sample.
8. (3 points). Suppose we want to estimate attrition rates among employees in state government, and we know that our target population is 65 percent male and 35 percent female. Our budget only allows a sample size of 100. We randomly sample 65 males and 35 females. This is an example of ________.
A) simple random sampling.
B) stratified random sampling.
C) cluster sampling.
D) judgment sampling.
9. (3 points). Find a confidence interval for ? assuming that the sample is from a normal population with known population standard deviation.
.0/msohtmlclip1/01/clip_image002.gif”>x = 20, ? = 3, n = 100, 95 percent confidence
A) (19.405, 20.595)
B) (17.412, 20.588)
C) (19.412, 20.588)
D) (19.412, 21.588)
10. (3 points). Find a confidence interval for ? assuming that the sample is from a normal population with unknown population standard deviation.
.0/msohtmlclip1/01/clip_image002.gif”>x = 20, s= 3, n = 100, 95 percent confidence
A) (18.412, 20.588)
B) (17.412, 20.588)
C) (19.412, 20.588)
D) (19.405, 20.595)
11. (3 points) Craig operates a part-time snow-plowing business using a 2002 GMC 2500 HD extended cab short box truck. Select the answer that best describes Craigs gasoline mileage based on this histogram of 195 tanks of gas.
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A. Craigs gas milage ranges from 10 to 18 miles per gallon.
B. Craigs gas milage ranges from approximately 8.5 to 22 miles per gallon with an average of approximately 14 miles per gallon.
C. Craigs gass milage ranges from 8.8 to 14.5 miles per gallon.
D. Craigs average milage is approximatly 19 miles per gallon.
Calculate the test statistic (t) and p-value for each sample mean (note: population variance is unknown):
12. .0/msohtmlclip1/01/clip_image005.gif”>(3 points) H0: µ ?200 versus H1: µ <200, ? = 0.05, x = 198, s = 5, n = 25 A) (t = -2.00, p-value = 0.0285) B) (t = 2.00, p-value = 0.0285) C) (t = -2.00, p-value = 0.9850) D) (t = -2.00, p-value = 0.0852) 13. (3 points) The average weight of a package of rolled oats is supposed to be at least 18 ounces. A sample of 18 packages shows a mean of 17.78 ounces with a standard deviation of 0.41 ounces. The calculated test statistic is t = -2.28 (left tail test) and the corresponding p-value = 0.018. Based on the results above, is the sample mean (17.78 ounces) smaller than the specification (18 ounces) at the 0.05 level of significance? (Check one of the following responses): A. Yes, the sample mean is significantly smaller than the specification at 0.05 level of significance. B. No, the sample mean is not significantly smaller than the specification at 0.05 level of significance. C. Yes, the p-value is greater than the alpha level. D. No, the p-value is lower than 0.01 14. (3 points) Which of the following comparisons would use a paired t-test? A. Fifteen retirees with diagnosed hypertension are assigned a program of diet, exercise, and meditation. A baseline measurement of blood pressure is taken before the program begins and again after 2 months. Was the program effective in reducing blood pressure of the participants after analyzing the mean blood pressure before the program compared to mean blood pressure after the program? B. Comparing average GPA of male undergraduate students vs. average GPA of female undergraduate students C. Comparing average age of juniors vs. average age of seniors. D. Comapring the average GPA of economics majors, biology majors, and computer science majors. 15. (3 points) Which of the following comparisons would use a t-test comparing two independent groups? A. Fifteen retirees with diagnosed hypertension are assigned a program of diet, exercise, and meditation. A baseline measurement of blood pressure is taken before the program begins and again after 2 months. Was the program effective in reducing blood pressure of the participants after analyzing the mean blood pressure before the program compared to mean blood pressure after the program? B. Comparing average GPA of male undergraduate students vs. average GPA of female undergraduate students C. Comparing average age of freshman, sophomores, juniors, and seniors. D. Comapring the average GPA of economics majors, biology majors, and computer science majors. Use the following information to answer the next question: A certain psychological theory predicts that men want bigger families than women. Kate asked each student in her psychology class how many children he or she considered ideal for a married couple, and obtained the Excel results shown below at .0/msohtmlclip1/01/clip_image007.gif"> = .05.
Hypothesis Test: Independent Groups (t-test, pooled variance)
Men
Women
2.24
2.03
mean
0.98
0.90
std. dev.
37
37
n
72
df
0.216
difference (Men – Women)
0.886
pooled variance
0.941
pooled std. dev.
0.219
standard error of difference
0
hypothesized difference
0.99
t
.3264
p-value (two-tailed)
16. (3 points) What conclusion can you draw from this analysis at .0/msohtmlclip1/01/clip_image007.gif”> = .05 assuming equal variances and using the results of the two-tailed test?
A) Men want larger families on average than women.
B) Women want larger families on average than men.
C) There appears to be no difference between the average size of families desired by men and women.
D) You need to determine if variances are equal or unequal before you can make a definitive conclusion.
Use the following information to to answer the next question: Mary did an analysis of acute care occupancy rates at two community hospitals and obtained the following results.
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17. (3 points) Which of the follow conclusions is correct? (Use ? = .05 and a the results of the two-tailed test)
A) There appears to be no difference in occupancy rates between the two hospitals.
B) HealthPro, on average, appears to have a significantly higher level of occupancy rate.
C) Mary has performed the wrong statistical test. She should have performed an ANOVA.
D) The table does not show enough information to make a decision.
Use the following information to answer the next question: Here is an Excel ANOVA table that summarizes the results of an experiment to assess the effects of ambient noise level and plant location on worker productivity. The test used ? = 0.05.
ANOVA table
Source
SS
df
MS
F
p-value
Noise Level
31.63
2
15.815
7.03
.0040
Error
54.00
24
2.250
Total
85.63
26
18. (3 points) The effect of noise level is significant.
A) True.
B) False.
Use the following information to answer the next three questions: A firm is studying the effect of work shift on its defect rate. The resulting ANOVA results are shown below.
ANOVA table
Source
SS
df
MS
F
p-value
Work Shift
8.00
2
4.000
0.94
.4064
Error
102.67
24
4.278
Total
110.67
26
19. (3 points) At ? = 0.01, the effect of shift is significant
A) True.
B) False.
20. (3 points) Based on the following MegaStat multiple comparison output, which day is most unusual? (Note: critical value = 2.42).
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A) Monday.
B) Wednesday.
C) Friday.
D) Thursday
21. (3 points) A scatter plot is used to visualize the association (or lack of association) between two quantitative variables.
A) True.
B) False.
22. (3 points) A correlation coefficient of r = 0.85, would indicate a strong positive relationship between two variables.
A) True.
B) False.
23. (3 points) A correlation of r = 0.40 indicates a stronger relationship than one of r = -0.60.
A) True.
B) False.
24. (3 points) The variable used to predict another variable in a regression analysis (usually X) is called the
A) response variable.
B) outcome variable.
C) independent variable.
D) dependent variable.
25. (3 points) The outcome variable (usually Y) in a regression analysis is called the
A) regression variable.
B) independent variable.
C) dependent variable.
D) dummy variable
William used a sample of 68 U.S. cities to estimate the relationship between Crime (annual property crimes per 100,000 persons) and Income (median income per capita). His estimated regression equation was
Crime = 428 – 0.05(Income).
26. (3 points) Assuming that b1 (slope) is significant, if Income increases by 1000 we would predict that Crime will:
A) increase by 428
B) decrease by 50
C) increase by 500
D) decrease by 500
Use the following multiple regression output to answer the next questions:
r²
0.233
n
19
r
-0.483
k
1
Std. Error
1.863
Dep. Var.
Crime
ANOVA table
Source
SS
df
MS
F
p-value
Regression
17.9268
1
17.9268
5.16
.0363
Residual
59.0205
17
3.4718
Total
76.9474
18
Regression output
confidence interval
variables
coefficients
std. error
t (df=17)
p-value
95% lower
95% upper
Intercept
8.4041
1.5801
5.319
.0001
5.0703
11.7379
Education
-0.7637
0.3361
-2.272
.0363
-1.4728
-0.0546
27. (3 points) What is the correct regression equation?
A. Education = 8.4041 0.7637(Crime)
B. Crime = 1.5801 + 0.3361(Education)
C. Crime = 5.319 2.272(Education)
D. Crime = 8.4041 0.7637(Education)
28. (3 points) Education is a significant predictor of Crime at ? = 0.05 significance level? (Circle one)
A) True.
B) False.
29. (3 points) As Education goes up, Crime goes (Circle one):
A. Down
B. Up
C. Stays the same
D. Not enough information
30. (3 points) How much variation is explained by this model? (Circle one)
A. 20.3%
B. 23.3%
C. 48.3%
D. 1.86%
31. (3 points) Select the best answer: What is the coefficient of determination?
A. The way to determine if you ran the right analysis.
B. The percent of variation explained in the independent variables that is explained by the dependent variable.
C.The percent of variation in the dependent variable that is explained by the independent variables.
D.The test statistic used to determine two group proportions.
Using the dataset provided (below), conduct a regression analysis.
Dependent Variable
Independent Variable 1
DV (Y)
IV1 (X)
100
4
110
6
115
5
125
7
133
6
144
8
155
8
165
9
155
8
176
9
165
7
179
12
32. (3 points) What is the regression coefficient (b1) for the independent variable? What is the associated p-value for the regression coefficient? Is the independent variable significantly related to the dependent variable at the p < 0.05 level? A. b1= 61.55; p-value = 0.0019; Yes, the IV is significantly related to the DV B. b1= 14.797; p-value = 4.160; No, the IV is not significantly related to the DV C. b1= 11.05; p-value = 0.0002; Yes, the IV is significantly related to the DV D. b1= 11.05; p-value = 1.925; No, the IV is not significantly related to the DV 33. (3 points) Calculate the regression equation Y = b0 + b1(X) A. DV = 61.55 + 11.05(IV1) B. DV = 14.80 + 1.93(IV1) C. DV = 4.16 + 5.74(IV1) D. DV = 28.58 + 6.76(IV1) 34. (3 points) Calculate the r2 value for the regression equation (above) A. 0.12 B. 0.15 C. 0.88 D. 0.77