QMM 280 - Example Test 2
MULTIPLE CHOICE:
1. As the confidence level increases from 95% to 99%, the width of
the confidence interval
a. increases
b. decreases
2. The probability of a Type I error and a Type II error are related
as follows:
a.
b.
c.
d.
>
>
as  increases  decreases
as  decreases  decreases
3. Which of the following statements is true?
a.
b.
c.
d.
e.
A parameter is the best estimate of .
, ² and  are all statistics.
A statistic estimates a parameter.
All parameters can function as a random variable.
None of the above.
4. The theorem which assures us that the distribution of the sample
mean approaches the normal distribution as the sample size
increases is called the
a.
b.
c.
d.
Central Limit Theorem.
Normal Probability Theorem
random selection process.
theorem of abnormality.
5. If we use  = .05 for a hypothesis test
a. the probability we
b. the probability we
hypothesis is true
c. the probability of
d.  = .95.
make an error is .025.
reject the null hypothesis when the null
is .95.
committing a Type I error is.05.
6. What are the two parameters for the population Regression Model?
a.
b.
c.
d.
α and β
µ and σ
β0 and β1
b1 and b2
7. A national standardized math test is know to have a mean score of
73 and standard deviation of 8.5. If all 33 students in your QMM
280 class take this test, what is the probability the class
average will be less than 71?
P ( X  71 )  P (
X  73
8 .5

33
71  73
8 .5
)  P ( Z   1 . 35 )  . 5  . 4115
 . 0885
33
8. OK-Mart is considering adding shopping carts for their retail
stores. Since you are the new management trainee, you have been
instructed to gather some sample data on the number of items a
customer buys while shopping at OK-mart. You randomly sample 40
customers and compute a sample mean of 5.47 and a standard
deviation of 3.18.
a. Construct a 99% confidence interval for the
population mean number of items purchased.
X  t n 1
sx
n
 5 . 47  2 . 576
3 . 18
 5 . 47  1 . 2952
40
I am 99% Confident the actual value of μx is in the
interval [4.1748,6.7652]
b. Management is upset with the width of the interval
in part a. They send you back to your office with
an order to come up with a smaller interval. How
would you accomplish this with the information you
have?
Lower the confidence level (increase α)
c. What trade off have you made?
We have a more precise estimate but we are less confident
that the interval will contain μx
d. How could you retain the same confidence level and decrease
the width of the interval?
Increase the sample size
9. Use the same data from problem 3;
a.
x = 5 .4 7 , s = 3 .1 8 , n = 4 0 .
Management would like you to test the
hypothesis Ho:  = 6.2. They decree an 
level of .01. Show all steps.
Step I Ho:  = 6.2
Ha:  ≠ 6.2
Step II
TS 
X  0
sx
 t n 1
n
Step III α = .01. Using the critical value approach:
Accept Ho if (-2.576  TS  2.576)
Reject Ho otherwise
Step IV TS = -1.45
Step V
Decision: Do not Reject Ho.
Conclusion: There is NOT sufficient evidence to
conclude the number of items customers buy at OK
Mart is different from 6.2.