Question

Decision (Reject or Fail to Rejeet) Conclusion (Answer the question posed) 40 of 50 male college students interviewed believe that the legal drinking age should be lowered from 21 to 18. Only 55 of 90 female college students believe that the drinking age should be lowered. Do males favor the change at a significantly higher rate than females? (α .05) 2. Ho Critical Value(s)- Test Value- Decision Conclusion-

Answer 1

H₀: P1 = P2

H₁: P1 > P2

$\widehat p1$ = 40/50 = 0.8

$\widehat p2$ = 55/90 = 0.61

At $\alpha$ = 0.05, the critical value is z_0.95 = 1.645

The pooled sample proportion(P) = ( $\widehat p1$ * n1 + $\widehat p2$ * n2)/(n1 + n2)

                                                     = (0.8 * 50 + 0.61 * 90)/(50 + 90)

                                                     = 0.68

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

      = sqrt(0.68 * (1 - 0.68) * (1/50 + 1/90))

      = 0.082

The test statistic z = ( $\widehat p1 - \widehat p2$ )/SE

                             = (0.8 - 0.61)/0.082

                             = 2.32

Since the test statistic value is greater than the critical value (2.32 > 1.645), so we should reject the null hypothesis.

So at $\alpha$ = 0.05, there is sufficient evidence to conclude that males favor the changes at a significantly higher rate than females.