Business Statistics MCQ Exam Solutions

Topics: Statistical hypothesis testing, Statistics, Statistical significance Pages: 6 (1354 words) Published: March 29, 2015
Sample Exam Solutions

Problem 1 (Hypothesis testing)
A company that manufactures travel goods is particularly concerned that the mean weight of the roll-on cabin bags should not exceed 3 kg as many airlines limit the weight of carry-on luggage on their planes to 7 kg. Past experience allows the assumption that the std. dev = 0.03 kg. A sample of 50 cabin bags is selected and the sample mean is 3.009 kg. Using a 0.05 significance, conduct a hypothesis test to determine if the population mean weight of the cabin bags is greater than 3kg?

What is the null and alternative hypothesis for this test?

AH0: µ ≥ 3, H1: µ < 3
BH0: µ ≤ 3, H1: µ > 3
CH0: µ = 3, H1: µ ≠ 3
DH0: µ ≠ 3, H1: µ = 3
ENone of the above
Ans: B

What is (are) the critical value(s)?

A-1.96 and 1.96
B-1.645
C-1.645 and 1.645
D1.645
ENone of the above
Ans: D

What is the calculated test statistic?
A 2.12
B 1.43
C 1.78
D 1.23
E None of the above

Ans: A

What is your conclusion? (choose the most correct answer)
A Reject Ho at the 5% level of significance.
B Accept Ho at the 5% level of significance.
C Not sure.
D None of the above.
E Need more information.
Ans: A

Calculate the p-value
A P value = 0.017
B P value = 0.09
C P value = 0.05
D Not sure
E None of the above.
Ans: A

Interpret the meaning of the p-value
A The probability of observing a test statistic more extreme than the observed sample value given the null hypothesis is true. B The observed level of significance.
C The smallest value of α for which H0 can be rejected.
D All of the above
E None of the above
Ans: D

Problem 2 (Multiple Regression):
A developer who specialises in holiday cottage properties is considering purchasing a large tract of land adjoining a lake. The current owner of the tract has already subdivided the land into separate building lots and has prepared the lots by removing some of the trees. The developer wants to forecast the value of each lot. From previous experience, she knows that the most important factors affecting the price of the lot are size, number of mature trees and distance to the lake. Y: price in thousands of dollars

X1: lot size in hundreds of square metres
X2: number of mature trees
X3: distance to the lake in metres

What is the best interpretation for the estimated coefficient for Trees?

AFor every additional tree, the estimated property price does not change BFor every additional tree, the estimated property price increases by $679 CFor every additional tree, the estimated property price increases by $0.679 DFor every additional tree, the estimated property price decreases by $679 ENone of the above

Ans: B

Does Lot-size have a statistically significant effect on property prices at the 5% level of significance? Why/Why not?

AYes, as the p-value is less than 0.05
BNo, because the t-stat is too low
CNo, because the p-value is less than 1.96
DNot enough information
ENone of the above

Ans: B

Interpret the 95% confidence interval associated with the coefficient Trees:

AIrrelevant as the number of mature Trees have a significant effect on property price BWe are 95% confident that number of mature Trees will increase property price by $700 CWe are 95% confident that a number of mature trees will increase property price between $220 and $1138 DWe are 95% confident that a a number of mature trees will increase property price between $600 and $800 ENone of the above

Ans: C

Interpret the R2

A24% of variation in property prices can be explained by variation in the X variables B76% of variation in property prices can be explained by variation in the Y variables C30.94% of variation in property prices can be explained by variation in the X variables D31.81% of variation in property prices can be explained by variation in the Y variables ENone of the above

Ans: A...
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