STAT212_093_01_E1 by panniuniu

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```									        STAT212_093_A                                                          Page 1 of 4

KING FAHD UNIVERSITY OF PETROLEUM & MINERALS
DEPARTMENT OF MATHEMATICS & STATISTICS
DHAHRAN, SAUDI ARABIA
STAT 212: BUSINESS STATISTICS II
Major Exam 1
10:30 pm –11:30 pm

Name:                                 ID#:                                    Serial:

Question No     Full Points         Points Obtained

1                10

2                20

3                10

Total              40
STAT212_093_A                                                    Page 2 of 4

Q1. (10 pts) Multiple Choice

1. If we are performing a two-tailed test of whether  = 100, the probability of detecting
a shift of the mean to 105 will be ________ the probability of detecting a shift of the
mean to 110.
a) less than
b) greater than
c) equal to
d) not comparable to

2. The number of degrees of freedom associated with the t test, when the data are
gathered from a matched pairs experiment with 15 pairs, is:
a) 30 b) 15 c) 28      d) 14

3. A major videocassette rental chain is considering opening a new store in an area that
currently does not have any such stores. The chain will open if there is evidence that
more than 5,000 of the 20,000 households in the area are equipped with videocassette
recorders (VCRs). It conducts a telephone poll of 300 randomly selected households in
the area and finds that 96 have VCRs. The p-value associated with the test statistic in
this problem is approximately equal to:

a)   0.0100
b)   0.0051
c)   0.0026
d)   0.0013

4. Suppose we wish to test H0:   47 versus H1:  > 47. What will result if we conclude
that the mean is greater than 47 when its true value is really 52?

a)   We have made a Type I error.
b)   We have made a Type II error.
c)   We have made a correct decision
d)   None of the above are correct.

5. We have created a 95% confidence interval for  with the result (10, 15). What
decision will we make if we test H0 :  16 versus H1 :   16 at  = 0.10?

a) Reject H0 in favor of H1.
b) Accept H0 in favor of H1.
c) Fail to reject H0 in favor of H1.
d) We cannot tell what our decision will be from the information given.
STAT212_093_A                                                           Page 3 of 4

Q2. (8+12=20 pts) A manufacturer uses two different trucking companies to ship its merchandise.
The manufacturer suspects that one company is charging more than the other and wants to test it. A
random sample of the amounts charged for one truckload shipment from Chicago to Detroit on
various days is collected for each trucking company. The data (I dollars) is given below.
∑X= 28855 , ∑X2=75994975                  , ∑Y= 21080 , ∑Y2=50613100
X=Comp1 2570 2480 2870 2975 2660 2380 2590 2550 2485 2585 2710
Y=Comp2 2055 2940 2850 2475 1940 2100 2655 1950 2115
a. Test the assumption of equal variance.
(1 pt) The hypotheses are:

(1 pts) Decision Rule:

(3 pts) The test statistic:

(2pts) Critical value(s):

(1pts) Conclusion:

b. Assuming that the two populations are normally distributed with equal variance, test the
null hypothesis that the two companies’ average charges are equal.
(2 pt) The hypotheses are:

(1 pts) Decision Rule:

(6 pts) The test statistic:

(1 pts) Critical value(s):

(2pts) Conclusion:
STAT212_093_A                                                             Page 4 of 4

Q3. (10 pts) A maker of toothpaste is interested in testing whether the proportion of adults (over age 18)
who use their toothpaste and have no cavities within a six-month period is any different than the
proportion of children (18 and under) who use the toothpaste and have no cavities within a six-month
period. To test this, they have selected a sample of adults and a sample of children randomly from the
population of those customers who use their toothpaste. The following results were observed.
Adults               Children
Sample Size                    100                   200
Number with 0 cavities          83                   165
Based on these sample data and using a significance level of 0.05, what conclusion should be reached.

(1 pt) The hypotheses are:

(1 pts) Decision Rule:

(5 pts) The test statistic:

(2 pts) Critical value(s):

(1pts) Conclusion:

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