## (solution) EC 315 Homework #2 1. You have been hired as the Quality Control

Looking for someone who would be able to complete the attached 3 documents....for a total of 15 questions by midnight tonight. The subject matter is Quantitative Research Methods. If interested please respond ASAP.

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EC 315

Homework

#2

1. You have been hired as the Quality Control Manager for a soft drink company.

Your

company has recently received numerous complaints concerning the seal on

two-liter bottles of soft drinks sold by your company. In order to form an

effective seal on the bottles, all caps must have an average diameter of 1.85 cm

with a standard deviation of 0.05 cm. If the average is lower, the caps won?t fit

on the bottles, and must be discarded. If the average is larger, the bottles can?t

be sealed effectively, and their contents will spoil. The Production Manager is

concerned about either of these potential outcomes, since they could increase

production costs if a large number of caps are discarded, or cause customer

complaints and returns if the contents spoil. To insure that you are using a large

sample, you take a random sample of 64 bottle caps and found them to have an

average diameter of 1.87. Test the assumption that the caps are properly sized

at the 1% significance level. Summarize your results below: (You must show all

work as well as appropriate distribution diagrams to receive credit)

A. H0:

H 1:

B. What is the appropriate test statistic? __________

C. State the decision rule, and sketch the distribution showing the region(s) of

acceptance and rejection.

D. State the statistical Decision. Show supporting calculations.

E. What recommendations would you make to the Production manager

concerning

the setting of the machine?

2. A company manufactures rocket engines used to launch satellites into space.

The government buys these rocket engines, and the contract specifies that the

average fuel consumption must be 5500 pounds in the first 15 seconds of

operation. If fuel consumption is significantly less than 5500 pounds, the thrust

will be insufficient for the launch. If it is significantly more, then the risk of

explosion at launch increases dramatically. The Director of Quality Control has

asked you to oversee a test of the engines, and to recommend corrective action

if necessary. You decide to use the Hypothesis Testing process to test the engines

1 EC 315

#2 Homework

since it useful in testing assumptions about a population. You take a random

sample of 6 engines since you only have a small number of engines in

production at any time. You fire each of them for 15 seconds and find that the

average fuel consumption is 5690 pounds with a standard deviation of 250

pounds. Does this result suggest that the contract provision on fuel consumption

is not being met at the 5% significance level?

A. H0:

H 1:

C. State the decision rule, and sketch the distribution showing the region(s) of

acceptance and rejection.

D. State the statistical Decision. Show supporting calculations. E. What recommendations would you make to the Director of Quality Control

Concerning the fuel consumption of the rockets?

3. A recent study by Consumer Reports showed that 64% of supermarket shoppers

believed that supermarket brands are as good as national brands. To test this

claim, the manufacturer of a national name brand ketchup took a sample of 100

shoppers and found that 52% stated that supermarket brands were as good as

the national brand.

A. Formulate the hypotheses required to test whether the percentage of

shoppers who believe supermarket were as good as national brands was less than 64%.

B. What is the appropriate test statistic? __________ Explain your answer. C. State the decision rule, and sketch the distribution showing the region(s) of

acceptance and rejection.

2 EC 315

Homework #2

D. State the statistical Decision. Show supporting calculations. E. What recommendations would you make to the Ketchup manufacturer

concerning the based on the results of the survey? 3

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