Question

QUESTION 21 An official of a large national union claims that the fraction of women in the union is not significantly different from 58%. To test this claim, a random sample of 400 individuals in the union is taken. Of those 400,215 are women. Suate the null and alternative hypotheses. Hop 50.58 and Hp>0.58 Ho ip 0.58 and Hp0.58 Hp <0.58 and Hp0.58 Od Hop20.58 and H:p<0.58 QUESTION 22 An official of a large national union claims that the fraction of women in the union is not significantly different from 585. To test this claim, a random sample of 400 individuals in the union is taken. Of those 400.215 are women Use the p-value to conduct the hypothesis test and use a = 0.05 level of significance. p-value 00446 <0.05: Fail to reject H. p-value 0.0146 <0.05: Reject H. p-value 0.4714>0.05Fail to reject H. MacBook 80 999

Answer 1

Q21:

Null and alternative hypothesis:

Ho : p = 0.58

H1 : p ≠ 0.58

Answer b.

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Q22:

n = 400

x = 215

p̂ = x/n = 0.5375

α = 0.05

Null and Alternative hypothesis:

Ho : p = 0.58

H1 : p ≠ 0.58

Test statistic:

z = (p̂ -p)/√(p*(1-p)/n) = (0.5375 - 0.58)/√(0.58 * 0.42/400) = -1.72

p-value = 2*(1-NORM.S.DIST(ABS(-1.72), 1)) = 0.0854

Decision:

p-value > α, Fail to reject the null hypothesis