Explanation Calculation: In a survey, of 909 U.S. adults who have children, 309 were found to be save their money for college. 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 909 is assumed to be 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, adults who save money for college and adults who do not save money for college. • Verify the condition: n p ^ 0 ≥ 10 and n q ^ 0 ≥ 10 Here, p ^ 0 = 309 909 = 0.34 Substitute n as 909 and p ^ as 0.34, n p ^ 0 = 909 ( 0.34 ) = 309.06 > 10 Substitute n as 909 and q ^ 0 as 0.66 ( = 1 − p ^ 0 ) , n q ^ 0 = 909 ( 0.66 ) = 599.94 > 10 Therefore, all the conditions are satisfied. Step 1: Denote p as the true population proportion of the U.S. adults with children that had saved money for college. The given test hypotheses are: Null hypothesis: H 0 : p = 0

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Chapter 8.5, Problem 11E

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Check whether it can be concluded that the proportion of the U.S. adults with children that had saved money for college is greater than 0.3.

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Chapter 8.5, Problem 10E

Chapter 8.5, Problem 12E

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