A magazine article reporting on a survey of the attitudes of men from a certain

Question

A magazine article reporting on a survey of the attitudes of men from a certain region, noted that "Young men are more comfortable than older men talking about their problems." The survey reported that 122 of 189 surveyed 18- to 24-year-old men and 59 of 110 surveyed 25- to 34-year-old men said they were comfortable. Is the magazine's interpretation justified by these numbers? Write the appropriate hypotheses to conduct a hypothesis test. Let p, be the proportion of 18- to 24-year-old men who are comfortable discussing their problems. Let p2 be the proportion of 25- to 34-year-old men who are comfortable discussing their problems. Choose the correct answer below OA. Ho: p1-P2-0 B. Ho: p1-P2#0 DHo: P1-P20 HA: P-P2-0 HA: P,-P2>0 Determine the test statistic. z(Round to two decimal places as needed.)

Explanation / Answer

p1 = 122/189 = 0.6455 , n1 = 189
p2 = 59/110 = 0.5364 , n2 = 110

p = (p1 * n1 + p2 * n2) / (n1 + n2)
= ( 0.6455 * 189 + 0.5364 * 110)/( 189 +110)
= 0.6054

SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
= sqrt(0.6054 * (1-0.6054) * ((1/189) +( 1/110)))
= 0.0586

z = (p1 - p2) / SE
= ( 0.6455 - 0.5364) / 0.0586
= 1.8618

p value = 0.0313 at 0.05 significance level

Reject the null hy[othesis

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