Explanation Calculation: In a survey, of 341 video gamers, 110 gamers prefer playing games on a console, rather than a computer or hand-held device. Assumptions for performing a hypothesis test for a population proportion: • The samples taken from the population are simple random samples. • The population is at least 20 times as large as the sample. • The samples in the population are divided into two categories. • The values of n p ^ 0 and n q ^ 0 should be greater than or equal to 10. Requirement check: • The sample of 341 gamers is assumed to be simple random samples. • The information about the population is not known. However, the population size is assumed to be more than 20 times as large as the sample. • The samples in the population seemed to be categorized into two parts. That is, gamers who prefer console and gamers who do not prefer console. • Verify the condition: n p ^ 0 ≥ 10 and n q ^ 0 ≥ 10 Substitute n as 341 and p ^ 0 as 0.323, n p ^ 0 = 341 ( 0.323 ) = 110.14 > 10 Substitute n as 341 and q ^ 0 as 0.677 ( = 1 − p ^ 0 ) , n q ^ 0 = 341 ( 0.677 ) = 230.857 > 10 Therefore, all the conditions are satisfied

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Chapter 8.4, Problem 18E

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Check whether it can be concluded that the proportion of the gamers prefer console is greater than 25%.

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Chapter 8.4, Problem 17E

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