Question

A random sample of 100 urban residents reveals that 50 believe in angels whereas in a random sample of 100 rural residents it is found that 65 believe in angels. We test the null hypothesis that the percentage of urban and rural residents who believe in angels is the same against the alternative that it is higher for rural residents. Based on this data, the corresponding test statistic is 2.165 and we reject the null hypothesis at a significance level α = 10%.

True False

Answer 1

Test Statistic :-
Z = ( p̂1 - p̂2 ) / √( p̂ * q̂ * (1/n1 + 1/n2) ))
p̂ is the pooled estimate of the proportion P
p̂ = ( x1 + x2) / ( n1 + n2)
p̂ = ( 65 + 50 ) / ( 100 + 100 )
p̂ = 0.575
q̂ = 1 - p̂ = 0.425
Z = ( 0.65 - 0.5) / √( 0.575 * 0.425 * (1/100 + 1/100) )
Z = 2.146

Test Criteria :-
Reject null hypothesis if Z > Z(α)
Z(α) = Z(0.1) = 1.282
Z > Z(α) = 2.1456 > 1.282, hence we reject the null hypothesis
Conclusion :- We Reject H0

False

Test statistic is not 2.165