In World Values Survey in 2005 people in different countries answered a question
ID: 3207637 • Letter: I
Question
In World Values Survey in 2005 people in different countries answered a question whether they were very happy. In Venezuela 55 out of 100 answered "yes" (earning 1st place in that category for Venezuela), in Nigeria 45 in 100 said "yes" (2d place) an in the USA 39 in 100 answered "yes" (it shares 7th place with several other countries). In your testing state the null and alternative hypotheses (explain the choice), the statistic, distribution and p-value. Test whether this relative ranking of Venezuela above the USA is supported by statistical evidence.Explanation / Answer
Given that,
sample one, x1 =55, n1 =100, p1= x1/n1=0.55
sample two, x2 =39, n2 =100, p2= x2/n2=0.39
null, Ho: p1 < p2
alternate, H1: p1 > p2
level of significance, = 0.05
from standard normal table,right tailed z /2 =
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 =(0.55-0.39)/sqrt((0.47*0.53(1/100+1/100))
zo =2.267
| zo | =2.267
critical value
the value of |z | at los 0.05% is 1.645
we got |zo| =2.267 & | z | =1.645
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: right tail - Ha : ( p > 2.2668 ) = 0.0117
hence value of p0.05 > 0.0117,here we reject Ho
ANSWERS
---------------
null, Ho: p1 = p2
alternate, ranking of Venezuela is above the USA H1: p1 > p2
test statistic: 2.267
critical value: 1.645
decision: reject Ho
p-value: 0.0117
we have evidnence to support ranking of Venezuela is above the USA
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