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# King Fahd University of Petroleum and Minerals

By Norman Allen,2014-05-14 00:46
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King Fahd University of Petroleum and Minerals

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Examples

1. Ten successively tested light bulbs functioned for the

following lengths of time (measured in hours):

36, 39, 18, 42 45, 35, 28, 24, 20, 40 Assuming that the measurements represent is a random

sample from a normal population.

?a. Given that =10, find a 95% confidence interval

estimate of the mean life of a light bulb.

b. Give a 90% confidence interval estimate of the mean

life of a light bulb.

c. A claim has been made that the results of this

experiment indicate, “One can be 90% confident that

the true mean life exceeds 30 hours.” Do you agree

with this statement? Explain. Note use your results in

part a.

2. The weight of salmon grown at a commercial hatchery

has a standard deviation of 1.2 pounds. The hatchery

claims that the mean weight is at least 7.6 pounds. A

random sample of 36 fish yielded and average weight of

8.2 pounds and 1.5 pounds as a standard deviation.

a. Is there is strong evidence to reject the hatchery’s

claims at the 1% level of significance? Use the p-value

method to test the hatchery’s claims.

b. Estimate the population mean of the salmon using

95% confidence level. And interpret your results.

3. Out of a random sample of 120 students at a

university, 12 stated that they were smokers.

a. Construct a 98% confidence interval estimate of the

true proportion of all the students at the university

who are smokers.

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b. How large a sample is needed to ensure that the

length of the 95% interval estimate of the true

proportion is within ??0.03? c. Test the claim that that the true proportion of

nonsmokers is less than 13%, use 1% level of

significance.

4. A high school is interested in determining whether two

of its instructors are equally able to prepare students for

countrywide examination in Statistics. Seventy two

students taking Statistics this semester were randomly

divided into tow groups of 36 each. Instructor 1 taught

Statistics to the first group, and instructor 2 to the

second group. At the end of semester, the students took

the countrywide examination, we get the following

results:

Mean Variance

Class 1 70.6 81.6

Class 2 74.2 36.2 Can you conclude from these results that the

instructors are not equally able in preparing students

for the examination? Use 5% and 1% level of

significances. Give the null and alternative hypotheses

and the resulting of the p-value. What are your final

conclusions?

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5. A taxi company is trying to decide whether to purchase

brand A or brand B tires for its fleet of taxis. To

estimate the difference in the two brands, an experiment

is conducted using a sample of 10 tires of each brand.

The tires are run until they wear out. The results are

Mean in K Standard deviation in K

Brand A 36,500 5,000

Brand B 39,300 7,100

Assume that the variances are equal.

a. Compute a 95% confidence interval for the

difference between the two population means.

b. Use 5% level of significant to test the null

hypothesis that there is no difference between the

two brands.

c. What are the assumptions that you need to answer

the above two questions.