Question

4) John believes that 50% of first-time brides in the United States are younger than their grooms. He performs a hypothesis test to test the claim that if the percentage is different from 50%. John samples 100 first-time brides and 53 reply that they are younger than their grooms. a0.01 (10 points) (a) What are the hypotheses? nc (b) Find the test statistic. (Show all your formula and work) (Round to two decimal places as needed.) (c) Find the p-value and interpret the result. (Show all your work) (Round to four decimal places). (d) State the final conclusion that addresses the original claim

Answer 1

Solution

(a) Hypothesis :

Null hypothesis , H0 : p = 0.5

alternate hypothesis , Ha : p $\neq$ 0.5

(b) z test stat = (p0 -p)/((p(1-p)/n)^0.5

p0 = 0.53

z = (0.53-0.5)/((0.5)(0.5)/100)^0.5 = 0.6

(c) p value = 0.5485 (two talied)

(d) do not reject the null hypothesis