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Hypothesis Test of Proportions

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The manufacturer of the ColorSmart - 5000 television set claims that 95 percent of its sets last at least five years without needing a single repair. In order to test this claim, a consumer group randomly selects 400 consumers who have owned a ColoSmart - 500 television set for five years. Of these 400 consumers, 316 say that their ColorSmart - 500 television sets did not need repair, while 84 say that their ColorSmart - 5000 television sets required did need at least one repair.

a. Letting p be the proportion of ColorSmart - 5000 television sets that last five years without a single repair, and set up the null and alternative hypothesis that the consumer group should use to attempt to show that the manufacturers claim is false.
b. Use rejection points and previously given sample information to test the hypothesis you set up in part a by setting alpha equal to 010, .05, .01, and .001. How much evidence is there that the manufacturer's claim is false?
c. Do you think the results of the consumer group's survey have practical importance? Explain your opinion.
d. Complete the exercise from the data given and answer all of the questions in a written summary. Cut and paste any EXCEL data that you wish to discuss.

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Solution Summary

The solution examines proportions hypothesis tests.

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