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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.

    What is your interpretation of your finding?

    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.

    d. What is your final conclusion about the difference

    between the two brands of tires?

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