Explanation Calculation: There are total of 450 purchases, among 202 are brand A computers, 175 are brand B computers and 73 are other type of computers. The level of significance is 0.05. The hypothesis to be tested is, H 0 : p = 0.50 H a : p ≠ 0.50 The proportion of people who purchase brand A is defined as p. The claim that brand A and brand B have the same share of the personal computer market is the null hypothesis. Thus, the alternative hypothesis is there is a difference in the share of the personal computer market for brand A and brand B. The hypotheses are given below: Null hypothesis: H 0 : p = 0.50 That is, brand A and brand B have the same share of the personal computer market. Alternative hypothesis: H a : p ≠ 0.50 That is, there is a difference in the share of the personal computer market for brand A and brand B. From the data, there are 202 + 175 = 377 computers of brand A and brand B. For a sign test the mean μ = 0.5 n and standard deviation σ = 0.25 n and n = 377 Substitute n = 377 The mean is, μ = 0.5 ( 377 ) = 188.5 Thus, the mean is 188.5. The standard deviation is, σ = 0.25 ( 377 ) = 94.25 = 9.7082 Thus, the standard deviation is 9.7082. There are 202 plus signs in the upper tail. The probability of 202 plus signs in the upper tail can be obtained by the continuity correction factor and normal approximation. Hence, the p -value is obtained by using normal distribution with μ = 188 .5 and σ = 9.7082 P ( 202 or more plus signs ) = P ( x ≥ 201

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Chapter 18.1, Problem 11E

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Conduct the required hypothesis test and make a conclusion.

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Chapter 18 Solutions

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Ch. 18.1 - 1. The following hypothesis test is to be...Ch. 18.1 - 2. Ten individuals participated in a taste test...Ch. 18.1 - 3. The median number of part-time employees at...Ch. 18.1 - 4. Net assets for the 50 largest stock mutual...Ch. 18.1 - Prob. 5E Ch. 18.1 - Prob. 6E Ch. 18.1 - Prob. 7E Ch. 18.1 - Prob. 8E Ch. 18.1 - Prob. 9E Ch. 18.1 - Prob. 10E

Ch. 18.1 - Prob. 11E Ch. 18.2 - 12. Two fuel additives are tested to determine...Ch. 18.2 - 13. A sample of 10 men was used in a study to test...Ch. 18.2 - Prob. 14E Ch. 18.2 - Prob. 15E Ch. 18.2 - Prob. 16E Ch. 18.2 - Prob. 17E Ch. 18.3 - Two fuel additives are being tested to determine...Ch. 18.3 - Samples of starting annual salaries for...Ch. 18.3 - The gap between the earnings of men and women with...Ch. 18.3 - Prob. 21E Ch. 18.3 - Prob. 22E Ch. 18.3 - Police records show the following numbers of daily...Ch. 18.3 - A certain brand of microwave oven was priced at 10...Ch. 18.3 - Prob. 25E Ch. 18.4 - A sample of 15 consumers provided the following...Ch. 18.4 - Three admission test preparation programs are...Ch. 18.4 - Prob. 28E Ch. 18.4 - Prob. 29E Ch. 18.4 - A large corporation sends many of its first-level...Ch. 18.4 - Prob. 31E Ch. 18.5 - Prob. 32E Ch. 18.5 - 33. Consider the following two sets of rankings...Ch. 18.5 - Prob. 34E Ch. 18.5 - Prob. 35E Ch. 18.5 - 36. The rankings of a sample of professional...Ch. 18.5 - Prob. 37E Ch. 18 - 38. A survey asked the following question: Do you...Ch. 18 - Prob. 39SE Ch. 18 - Prob. 40SE Ch. 18 - Prob. 41SE Ch. 18 - Prob. 42SE Ch. 18 - Prob. 43SE Ch. 18 - Prob. 44SE Ch. 18 - Prob. 45SE Ch. 18 - Prob. 46SE Ch. 18 - Prob. 47SE

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Conduct the required hypothesis test and make a conclusion.

Solution Summary: The author concludes that there is a difference in the share of the personal computer market for brand A and brand B.

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Conduct the required hypothesis test and make a conclusion.

Chapter 18 Solutions