Question

In a recent survey of drinking laws, a random sample of 1000 women showed that 65% were in favor of increasing the legal drinking age. In a random sample of 1000 men , 60% favored increasing the legal drinking age. Test the hypothesis that the percentage of women favoring a higher legal drinking age is greater than the percentage of men. Use a= 0.05

Call women population 1 and men population 2

A) What initial conclusion would be reached in this hypothesis test?

a. Reject H₁

b. Reject H₀

c. Do not reject H₀

d. Do not reject H₁

B) What is the possible error type and the correct statement of the possible error?

a. Type 1: The sample data indicated that the proportion of women in favor of increasing the drinking age is greater than the proportion of men, but actually the proportion is less than or equal to.

b. Type 2: The sample data indicated that the proportion of women favoring a higher drinking age is equal to the proportion of men, but actually the proportion of women is greater.

c. Type 2: The sample data indicated that the proportion of women who favor a higher drinking age is less than the proportion of men, but actually the proportions are equal.

d. Type 1: The sample indicated that the proportion of women who favor a higher drinking age is greater than the proportion of men, but actually the proportion of men favoring a higher drinking age is greater.

C) State the conclusion in a sentence.

Answer 1

Given that,
sample one, x1 =650, n1 =1000, p1= x1/n1=0.65
sample two, x2 =600, n2 =1000, p2= x2/n2=0.6
null, Ho: p1 = p2
alternate, H1: p1 > p2
level of significance, α = 0.05
from standard normal table,right tailed z α/2 =1.645
since our test is right-tailed
reject Ho, if zo > 1.645
we use test statistic (z) = (p1-p2)/√(p^q^(1/n1+1/n2))
zo =(0.65-0.6)/sqrt((0.625*0.375(1/1000+1/1000))
zo =2.309
| zo | =2.309
critical value
the value of |z α| at los 0.05% is 1.645
we got |zo| =2.309 & | z α | =1.645
make decision
hence value of | zo | > | z α| and here we reject Ho
p-value: right tail - Ha : ( p > 2.3094 ) = 0.01046
hence value of p0.05 > 0.01046,here we reject Ho
ANSWERS
---------------
null, Ho: p1 = p2
alternate, H1: p1 > p2
test statistic: 2.309
critical value: 1.645
A.
decision: reject Ho
option:b
p-value: 0.01046
B.
a. Type 1: The sample data indicated that the proportion of women in favor of increasing the drinking age is greater than the proportion of men, but actually the proportion is less than or equal to.
C.
we have enough evidence to support the claim that the percentage of women favoring a higher legal drinking age is greater than the percentage of men