Self Test 7 for Probability and Statistics

This test was constructed based
on the Schaum's Outline *Theory and Problems of Probability and Statistics*
by Murray R. Spiegel. If you need more review refer also to this outline.

*Tests of Means and Proportions Using Normal Distributions*

**1. True
False.** The mean life time of a sample of 100
light bulbs produced by a certain company is computed to be 1550 hours with a
standard deviation of 120 hours. If μ is the mean lifetime of all the
bulbs produced by the company, test the hypothesis μ =1600 hours against
the alternative hypothesis μ ≠1600 hours, using 5% level of
significance.

a)Reject

(Contributed by Zauresh Atakhanova)

**2. True
False **The
mean service lives from a sample of 25 new, heavy-duty ore trucks from purchase
to their first major repair is computed to be 3200 hours. The standard
deviation is known at 250 hours. If m is the mean service time of all the trucks
of that model, test the hypothesis m=3100 hours against the alternative
hypothesis μ ≠3100 hours, using 5% level of significance.

We conclude that we must reject the null hypothesis at the 5% level of significance,
i.e. that the mean time until major repair is not 3100 hours. (Contributed by
James Golden)

**3. True
False.** In problem 1 test the hypothesis m=1600
hours against the alternative m<1600, using a 5% level of significance.

a) Reject

(Contributed by James Golden)

**4. True False**
Suppose that a random variable Y is such Y~ N(34.8,280). In addition suppose
that you are unaware that E(Y) = b = 34.8, and that you wish to use a random sample of 60
observations to test.

H_{o}= b = 30
against

H_{1 }= b >
30

If you use a %5 significance level, then the probability of making a Type I error is 0.987.

(Contributed by Carlos Roman)

**5. True
False**. A test was given to two classes
consisting of 50 and 60 students respectively. In the first class the mean
grade was 75 with standard deviation of 8. In the second class the mean grade
was 78 with standard deviation of 7. Is the performance of the two classes
significantly different at 1% and 5% level?

(a) No difference at both 1% and 5% significance level

(Contributed by Carlos Roman)

**6. True
False **You
have been monitoring crude oil production in

**7. True
False**. In the past a machine produced pieces of
equipment with a mean thickness of 0.060 inches. To determine whether the
machine is in the proper working condition, a sample of ten pieces of equipment
is chosen for which the mean thickness is 0.063 and the standard deviation is
0.003 inches. You should reject the hypothesis that the machine is in the
proper working condition using a level of significance of 0.05 but fail to
reject at a 1% significance level.

(Contributed by Maria Sanchez)

**8. True
False **A
directional drilling tool is designed to build angles at a rate of 0.100 degrees/foot.
To determine whether the machine is in the proper working condition, sixteen
wells are sampled for which the sample mean build rate is 0.106 and the
standard deviation is 0.012 degrees/foot. testing wheter your should expect
more than a 0.100 build rate? using a level of significance 0.05 and 0.01.

** **

After testing, the hypothesis that the machine is in the proper working
condition you fail to reject H_{0} at the 5% and 1% significance
levels.

(Contributed by James Golden)

**9. True
False **In
the past a machine produced pieces of iron with a mean thickness of 0.25
inches. To determine whether the machine is in proper working condition a
sample of 15 pieces of iron are chosen for which the mean thickness is 0.28 and
the standard deviation is 0.03 inches. Is the machine in the proper working
condition using a level of significance of 0.05 and 0.01 we can reject al %%
and fail to reject at 1% level of significance. (Contributed by Maria Sanchez)

**10. True
False** In the past the standard deviation of
weights of certain 40.0 gram packages filled by a machine was 0.25 grams. A
random sample of 30 packages showed a standard deviation of 0.32 grams. The
apparent increase in variability is significant at 0.05 level? (Contributed by Maria Sanchez)

**11. True
False **A professor has two classes, X and Y.
Class X had 16 students and class Y has 25 students. On the same test, although
there was no significant difference in mean grades, class X had a standard
deviation of 10 while class Y had a standard deviation of 13. We can conclude
at 1% level of significance, that the variability of class Y is greater than
that of X? (Contributed by Maria
Sanchez)

**12. True
False**. In 200 tosses of a coin, 116 heads and 84
tails were observed. Can we fail to reject testing the hypothesis that the coin
is fair using a level of significance of 0.05. (Contributed by Maria Sanchez)

**13. True
False** In the past a machine produced pieces of
equipment with a mean thickness of 0.060 inches. To determine whether the
machine is in the proper working condition, a sample of ten pieces of equipment
is chosen for which the mean thickness is 0.063 and the standard deviation is 0.003
inches. A two-tailed test using a level
of significance 0.05 is required to show that the machine is in the proper working condition.
(Contributed by Herman Logsend)