MATH30 - Long Quiz #3 - 3rd TERM - 20112012


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.

0 comments:

Post a Comment