1BUEC 333
Summer 2001
D. Maki
                     MIDTERM EXAMINATION - A
                              
Important - record on the top front of your answer sheet the letter "A", "B" or "C" from the examination title above.

This examination consists of 15 multiple choice questions, with a value of 5 points each, for a total of 75 points on the examination.  Choose the letter corresponding to the one best answer to each question.  Your grade will be computed on the basis of the number of correct answers.  The exams will be machine graded, and making the answers legible to the machine is your responsibility.  Use soft pencil (HB or softer) only.  Fill in the appropriate circles corresponding to your name on the answer sheet.  This is a closed book examination - no notes are allowed.  A formula  sheet and tables are attached.  Total time allowed = 50 minutes.  Infinite populations are assumed in all questions where population size is relevant.

Questions 1 - 4 refer to the following information.  Audie O'Fyle want to compare two compact disc players for backgrouhd noise.  Since different compact discs have different levels of noise, Audie selects six compact discs, plays them on each player. and records the average level of background noise for each.  The results are:

DISK          1     2     3     4     5     6
PLAYER 1      3     5    12     1     4     5
PLAYER 2      5     7    10     3     4     7

1.  Testing whether the two players differ on mean background noise, the appropriate distribution to use is:
a.  z (standard Normal)
b.  t with 11 degrees of freedom
c.  t with 10 degrees of freedom
d.  t with 5 degrees of freedom
e.  Chi-square

2.  Using a sign test to see if the means differ by player the p-value is:
a.  between 20 and 35%
b.  between 10 and 20%
c.  between 5 and 10%
d.  between 1 and 5%
e.  none of the above

3.  Testing whether the variances of the two players is equal the calculated test statistic is:
a.  between 5 and 6
b.  between 4 and 5
c.  between 3 and 4
d.  between 2 and 3
e.  between 1 and 2

4.  Using the Wilcoxon test to test whether the players differ as to mean background noise, the value of the calculated test statistic, T, is:
a.  1
b.  2
c.  3
d.  4
e.  none of the above

5.  To test whether her hogs' average weight was greater than 425 kg, a farmer took a sample of size 4, recording the weights:  550, 600, 400, 450 kg.  What is the p-value for this test?
a.  about 50%
b.  about 20%
c.  about 10%
d.  about 5%
e.  about 1%

6.  The Gizmo Company's Whoozit-producing machine may be improperly adjusted.  If properly adjusted, only 1 in 50 Whoozits produced are defective, otherwise more than 1 in 50 are defective  Of 250 Whoozits, 7 were defective.  What is the p-value for this test?
a.  almost 1
b.  about 0.50
c.  between 0.30 and 0.50
d.  about 0.05
e.  0.1841

7.  To test whether the proportion of red marbles in a bag is at least equal to the advertised 40%, the Marvel Marble Company draws a sample of size n=40 and rejects the null hypothesis if the sample proportion is less than 0.20.  What is beta if the true proportion is 0.25?
a.  zero
b.  over 50%
c.  between 10 and 20%
d.  less than 10%
e.  between 20 and 50%

Questions 8 - 10 refer to the following information.  A frequent flyer wants to test whether Cheapo Airlines provides passengers with bags of almonds containing the same number of nuts as other airlines.  He gets 100 passengers on a given flight to count the nuts in their bags.

Number of nuts per bag            5     6     7     8
Probability (other airlines)     .2    .4    .3    .1
Cheapo Airlines sample           32    47    16     5

8.  What is the expected number of bags containing 7 almonds?
a.  30
b.  33
c.  27
d.  25
e.  none of the above

9.  What is the value of the calculated test statistic?
a.  11.73
b.  22.79
c.  30.92
d.  17.46
e.   6.81

10.  Testing at the 5% level, the critical value is:
a.  5.99
b.  7.81
c.  9.35
d.  9.49
e. 11.14

11.  The main use of the Bowman-Shelton test is:
a.  to detect inequalities in the average values of different groups
b.  to detect if the variables involved are independent of each other
c.  to see if the probability of an event occurring in a time interval is the same for all equal-sized intervals
d.  to tell whether a parametric or non-parametric test should be used
e.  to see whether the number of occurrences in different time intervals are independent of each other

12.  In testing to determine whether prep school and public school graduates have different mean SAT scores, an admissions officer at Mann-Whitney University sampled 20 prep school and 30 public school graduates from the incoming freshman class.  The sum of the public school students' ranks was 670.  What is the U statistic for this test?
a.  140
b.  395
c.  460
d.  670
e. 1275

13.  Which of the following statements is correct?
a.  Type I and II errors can be made smaller by lengthening the acceptance region
b.  a large acceptance region ensures a low beta, but a high alpha
c.  a large acceptance region ensures a high beta, but a low alpha
d.  setting the significance level very low affects only the acceptance and not the rejection region
e.  none of the above is correct

14.  The sampling distribution of the difference between two means from independent samples
a.  is just a probability distribution for (xbar1-xbar2)
b.  is based upon repeated sampling of two populations
c.  has an S equal to an algebraic combination of the two standard errors
d.  assumes equal variances for the two populations
e.  all of the above

15.  Dr. I. M. Payne, a statistical dentist, will fire one of his two receptionists if the proportion of times he catches one not working is statistically different from the other, at the .01 significance level.  Of the 30 times he checked on Sally Sluff she was not working 14.  Of the 40 times he checked on Blanche Knott she was not working 21.  Does Dr. Payne fire a receptionist?
a.  no, since .058 is less than .311
b.  yes, since .058 is less than .062
c.  yes, since .058 is less than .311
d.  no, since .058 is less than .062
e.  yes