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According to Gartner Inc., the largest share of the worldwide PC market is held by Hewlett-Packard with 18.4%. Suppose that a market researcher believes that Hewlett Packard holds a higher share of the market in the northern region of Europe. To verify this theory, he randomly selects 428 people who purchased a personal computer in the last month in the northern region of Europe. Eighty-four of these purchases were Hewlett-Packard computers. Using a 1% level of significance, test the market researcher’s theory. What is the probability of making a Type I error? If the market share is really 0.21 in the north-west region of Europe, what is the probability of making a Type II error?
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Living Alone? In 2000, 25.8% of Americans 15 years of age or older lived alone, according to the Census Bureau. A sociologist, who believes that this percentage is greater today, conducts a random sample of 400 Americans 15 years of age or older and finds that 164 are living alone.
(a) If the proportion of Americans aged 15 years or older living alone is 0.258, compute the following expected numbers: Americans 15 years of age or older who live alone; Americans 15 years of age or older who do not live alone.
(b) Test the sociologist’s belief at the  level of significance using the goodness-of-fit test.
(c) Test the belief by using the approach presented in Section 10.2.
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