Do males have a higher approval rating of the President of the United States tha

Question

Do males have a higher approval rating of the President of the United States than females? Suppose 500 random male adults and 500 random female adults from the U.S. are asked to identify their overall satisfaction with their President on a scale from 1 to 10. Let population 1 be adult male U.S. citizens, and let population 2 be adult female U.S. citizens. The sample mean for the sample of males is 4.7 and the sample mean for the sample of females is 4.6. The standard deviation for the sample of males is 2.5 and the standard deviation for the sample of females is 1.9.

Explanation / Answer

Q1.

Given that,
mean(x)=4.7
standard deviation , s.d1=2.5
number(n1)=500
y(mean)=4.6
standard deviation, s.d2 =1.5
number(n2)=500
null, Ho: u1 < u2
alternate, H1: u1 > u2
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.648
since our test is right-tailed
reject Ho, if to > 1.648
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =4.7-4.6/sqrt((6.25/500)+(2.25/500))
to =0.767
| to | =0.767
critical value
the value of |t | with min (n1-1, n2-1) i.e 499 d.f is 1.648
we got |to| = 0.76696 & | t | = 1.648
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value:right tail - Ha : ( p > 0.767 ) = 0.22173
hence value of p0.05 < 0.22173,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 > u2
test statistic: 0.76696
critical value: 1.648
decision: do not reject Ho
p-value: 0.22173
male have a higher approval rating of the president of the united
states than females

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