The World Values Survey has asked if homosexuality is justifiable, on a scale fr

Question

The World Values Survey has asked if homosexuality is justifiable, on a scale from 1 ("never") to 10 ("always"). In 1981-1984 surveys in the United States of 2325 subjects in the United States had a mean response of 2.4 and a standard deviation of 2.3. In the 2010-2014 surveys, the United States of 2232 subjects in the United States had a mean response of 5.4 and a standard deviation of 3.4. A report about the results stated "The mean tolerance level for intolerance was 3 units higher in 2010-2014 than in 1981-1984. If the true means were equal, a difference of this size could be expected less than 0.01% of the time. For samples of this size, 95% of the time one would expect this difference in means to be within 0.2 of the true value." (q7.49)

Explanation / Answer

Given that,
mean(x)=2.4
standard deviation , 1 =2.3
number(n1)=2325
y(mean)=5.4
standard deviation, 2 =3.4
number(n2)=2232
null, Ho: u1 = u2
alternate, H1: 1 < u2
level of significance, = 0.05
from standard normal table,left tailed z /2 =1.64
since our test is left-tailed
reject Ho, if zo < -1.64
we use test statistic (z) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
zo=2.4-5.4/sqrt((5.29/2325)+(11.56/2232))
zo =-34.747
| zo | =34.747
critical value
the value of |z | at los 0.05% is 1.64
we got |zo | =34.747 & | z | =1.64
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: left tail - Ha : ( p < -34.747 ) = 0
hence value of p0.05 > 0,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: 1 < u2
test statistic: -34.747
critical value: -1.64
decision: reject Ho
p-value: 0
we have enough evidence to support the claim

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