Question

Write a full hypothesis test for the following: (hypothesis statement, verify conditions for CLT, test type and tail direction, fully representative graph (Pop. mean/prop, std err, ????̅ /????�, rejection region, ????), pvalue, conclusion, error type)

4. In a survey of 875,000 males who completed high school during the past 12 months, 65.8% were enrolled in college. In a survey of 901,000 females who completed high school during the past 12 months, 66.1% were enrolled in college. At ?? = 0.05 can you support the claim that the proportion of males who enrolled in college is less than the proportion of females who enrolled in college?

Answer 1

H₀: P1 = P2

H₁: P1 < P2

The pooled sample proportion(P) = ( * n1 + * n2)/(n1 + n2)

                                                     = (0.658 * 875000 + 0.661 * 901000)/(875000 + 901000)

                                                     = 0.6595

SE = sqrt(P(1 - P)(1/n1 + 1/n2))

     = sqrt(0.6595 * (1 - 0.6595) * (1/875000 + 1/901000))

     = 0.0007

The test statistic z = ()/SE

                            = (0.658 - 0.661)/0.0007

                            = -4.29

At alpha = 0.05, the critical value is z_0.05 = -1.645

Since the test statistic value is less than the critical value(-4.29 < -1.645), so we should reject H₀.

At alpha = 0.05, there is sufficient evidence to support the claim that the proportion of males who enrolled in college is less than the proportion of females who enrolled in college.