Explanation Calculation: In a random sample of 120 law students, 54 are found to be women. The researcher is interested to test the proportion of law students that are women. Thus, in this context, the parameter of interest is population proportion. 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 120 is simple random sample. • 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, students that are women and students those are not women. • Verify the condition: n p ^ 0 ≥ 10 and n q ^ 0 ≥ 10 Here, p ^ 0 = 54 120 = 0.45 Substitute n as 120 and p ^ as 0.45, n p ^ 0 = 120 ( 0.45 ) = 54 > 10 Substitute n as 120 and q ^ 0 as 0.55 ( = 1 − p ^ 0 ) , n q ^ 0 = 120 ( 0.55 ) = 66 > 10 Therefore, all the conditions are satisfied. Step 1: Denote p as the true population proportion of law students that are women. The given test hypotheses are: Null hypothesis: H 0 : p = 0

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Author: Navidi

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Chapter 8.5, Problem 8E

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Identify the parameter of interest.

Check whether it can be concluded that the proportion of law students that are women is less than 0.5.

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Chapter 8.5, Problem 7E

Chapter 8.5, Problem 9E

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Identify the parameter of interest. Check whether it can be concluded that the proportion of law students that are women is less than 0.5.