I.
TRUE OR FALSE
The
following statements are vital in strengthening your discernment on aspects of
decision making through the process of PROBABILITY
AND STATISTICS. Write TRUE if the statement suffices affirmation that
substantiates the claims while FALSE if the statement nullifies the assertions.
(1 point each)
1. A
sampling distribution is an assertion or conjecture concerning one or more
populations.
2. Failure
to reject a hypothesis merely implies that the data gives sufficient evidence
to disprove it.
3. Rejection
of a hypothesis means that there is a small probability of obtaining the sample
information observed when, in fact, the hypothesis is true.
4. The
last number that we observe in passing from the acceptance region into the
critical region is called the critical value.
5. Rejection
of the null hypothesis when it is true is called Type I Error.
6. Acceptance
of the null hypothesis when it is false is called Type II Error.
7. Sometimes,
the level of confidence is called the size of the test.
8. The
power of a test is the probability of rejecting Ho
given that a specific alternative is true.
9. A
P-Value is the lowest level of significance at which the observed value of the
test statistic is significant.
10. A
confidence interval is a prediction interval of a future observation.
II.
PROBLEM SOLVING
The
decision making process can be applied in a variety of everyday situations and
across most academic disciplines. In the following applications, you are going
to execute what you relatively understood from the fundamental analysis. (15
points each)
1.
A manufacturer of paper used for
packaging high quality cement requires a minimum strength of 20 pounds per
square inch. To check on the quality of it, a random sample of 10 pieces is
selected each hour from the previous hour’s production and a strength
measurement is recorded for each. The standard deviation of the strength of
measurements is known to 2 pounds per square inch and the strength measurements
are normally distributed.
(a) What is the approximate sampling
distribution of the sample mean of 10 test pieces of paper?
(b) If the mean of the population of strength
measurements is 21 pounds per square inch, what is the approximate probability
that, for a random sample of n =
10 test pieces of paper,
<
20?
(c) What would you select for the mean paper
strength in order that P(
<
20) be equal to 0.001?
2.
A random sample of n
measurements is selected from a population with unknown mean and known standard
deviation of 10. Calculate the width of 95% confidence interval for the mean
for these values:
(a) when
n =
200;
(b) when
we double the sampling size in (a).
(c) Compare
the widths of 90%, 95%, and 99% confidence interval for the mean using the same
sampling size in (a). What effect does increasing the confidence coefficient
have on the width of the confidence interval?
3.
Producers of polyvinyl plastic pipe
want to have a supply of pipes sufficient to meet marketing needs. They wish to
survey wholesalers who buy polyvinyl pipe in order to estimate the proportion
who plan to increase their purchases next year. What sample size is required if
they want their estimate to be within 0.04 of the actual proportion with
confidence coefficient of 0.90? Assume that the sample is large enough, a
success rate of 0.5 would yield the largest possible solution for n.
4.
A
random sampling of the QGC construction firm’s monthly operating expenses for
36 months produce a sample mean of Php 229,908.00 and a standard deviation of
Php 32,088.00. Determine a 90% upper confidence bound for the company’s mean
monthly expense.
5.
The
mean breaking strength of cables excellent for catenary bridge supplied by a
manufacturer is 1800 psi with a standard deviation of 100 psi. By a new
technique in the manufacturing process, it is claimed that the breaking
strengths of the cables have increased. In order to test the claim, a sample of
50 cables is tested. It is found that the mean breaking strength is 1850 psi.
Can we support the claim at 0.01 level of significance?
6.
A
random sample of 20 CE graduate students obtained a mean of 72 and a variance
of 16 on the licensure exam given by the Philippines Regulatory Commission.
Assuming that the scores to be normally distributed, construct a 95% confidence
interval for the standard deviation.
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