Explanation Calculation: The information was about the survey done on the free access to new sports channel for a period of one month. In survey, of 400 television viewers, 25 will pay extra $10 per month to continue the trial. 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 400 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, viewers who pay for the channel and viewers who do not pay for the channel. • Verify the condition: n p ^ 0 ≥ 10 and n q ^ 0 ≥ 10 Substitute n as 400 and p ^ 0 as 0.0625, n p ^ 0 = 400 ( 0.0625 ) = 25 > 10 Substitute n as 400 and q ^ 0 as 0.9375 ( = 1 − p ^ 0 ) , n q ^ 0 = 400 ( 0.9375 ) = 375 > 10 Therefore, all the conditions are satisfied

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Chapter 8.4, Problem 24E

To determine

Check whether the director’s claim that the proportion of the viewers who pay for the channel is more than 5% is true.

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Chapter 8.4, Problem 23E

Chapter 8.4, Problem 25E

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