Question

Ho & Ha , alpha Test Statistic, P-value or Critical Value, Conclusion, Statements that identifies Type 1 error and Type 11 errors for the givine problem.

1) In a random sample of 360 women, 65% favored stricter gun control laws. In a random sample of 220 men, 60% favored stricter gun control laws. Test the claim that the proportion of women favoring stricter gun control is higher than the proportion of men favoring stricter gun control. Use a significance level of 0.05.

Answer 1

Given that,

p1= 0.65 ,n1= 360

p2 = 0.60 , n2=220

Hypothesis Test:

null hypotheses:H₀: P1 = P2

Alternative hypotheses:H₁: P1 > P2

we know that,

test statistics=z= (p1 - p2)/SE

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

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

                                                      = (0.65 * 360 + 0.60 * 220)/(360 + 220) = 0.631

SE = sqrt(0.631 * (1 - 0.631) * (1/360 + 1/220))= 0.041

Then,

Z = (0.65 - 0.60)/0.041 = 1.22

P-value = P(Z > 1.22) = 1 - P(Z < 1.22) = 1 - 0.8888 = 0.1112

As the P-value is greater than the significance level (0.1112 > 0.05), so the null hypothesis is not rejected.

So there is not sufficient evidence to support the claim that the proportion of women favoring stricter gun control is higher than the proportion of men favoring stricter gun control.