Question

The numbers of online applications from simple random samples of high school applications for 1992 and for the 1998 were taken. In 1992, out of 442 applications, 181 of them were completed online. In 1998, out of 473 applications, 154 of them were completed online. Test the claim that the proportion of online applications in 1998 was equal to than the proportion of online applications in 1992 at the .01 significance level.

Claim:

Opposite:

The test is: (Right, left, two tailed)

Z= (Test statistic)

The critical values are:

Based on this information we?

Conclusion:

Answer 1

To Test :-

H0 :- P1 = P2
H1 :- P1 ≠ P2

It is two tailed test

p̂1 = 181 / 442 = 0.4095
p̂2 = 154 / 473 = 0.3256

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 = ( 181 + 154 ) / ( 442 + 473 )
p̂ = 0.3661
q̂ = 1 - p̂ = 0.6339
Z = ( 0.4095 - 0.3256) / √( 0.3661 * 0.6339 * (1/442 + 1/473) )
Z = 2.6332

Critical values  Z(α / 2) = Z(0.01 / 2) = ±2.576

Z < - 2.576 OR Z > 2.576

Test Criteria :-
Reject null hypothesis if Z > Z(α/2)
Z(α / 2) = Z(0.01 / 2) = 2.576
Z > Z(α/2)) = 2.6332 > 2.576, hence we reject the null hypothesis
Conclusion :- We Reject H0

There is not sufficient evidence to support the claim that the proportion of online applications in 1998 was equal to than the proportion of online applications in 1992.