Question

The numbers of online applications from simple random samples of college applications for 2003 and for the 2009 were taken. In 2003, out of 312 applications, 97 of them were completed online. In 2009, out of 316 applications, 78 of them were completed online. Test the claim that the proportion of online applications in 2009 was equal to than the proportion of online applications in 2003 at the .10 significance level.

Claim: Select an answer u 1 ≤ u 2 u 1 = u 2 p 1 < p 2 u 1 < u 2 p 1 ≤ p 2 p 1≠p 2 u 1 > u 2 p 1 = p 2 u 1≠u 2 u 1 ≥ u 2 p 1 ≥ p 2 p 1 > p 2  which corresponds to Select an answer H1: u 1 > u 2 H0: u 1 ≤ u 2 H1: u 1 < u 2 H0: p 1 = p 2 H1: p 1 < p 2 H1: p 1 > p 2 H1: u 1≠u 2 H0: p 1 ≤ p 2 H1: p 1≠p 2 H0: p 1≠p 2

Opposite: Select an answer u 1 = u 2 p 1 > p 2 u 1 < u 2 p 1 ≤ p 2 p 1≠p 2 u 1 ≥ u 2 u 1 ≤ u 2 u 1 > u 2 p 1 ≥ p 2 p 1 = p 2 u 1≠u 2 p 1 < p 2  which corresponds to Select an answer H1: u 1 <= u 2 H0: u 1 > u 2 H1: u 1 ≥ u 2 H0: u 1≠u 2 H1: u 1 = u 2 H0: p 1 = p 2 H1: p 1 > p 2 H0: p 1≠p 2 H0: p 1 ≤ p 2 H1: p 1≠p 2 H1: p 1 < p 2

The test is: Select an answer /right-tailed / two-tailed / left-tailed

The test statistic is: z = Select an answer 1.79 / 1.95 / 1.47 / 2.28 / 2.05  (to 2 decimals)

Based on this we: Fail to reject the null hypothesis / Accept the null hypothesis / Reject the null hypothesis / Cannot determine anything

Conclusion There Select an answer ( does / does not ) appear to be enough evidence to support the claim that the proportion of online applications in 2009 was equal to than the proportion of online applications in 2003.

The critical value is: z a/ 2= ±± Select an answer / 1.64 / 1.44 / 1.64 / 1.28 / 1.15  (to 2 decimals)

Answer 1

P1 :- Proportion of college applications for 2009

P2 :- Proportion of college applications for 2003

To Test :-

H0 :-  p 1 = p 2

H1 :- p 1 ≠ p 2

The test is / two-tailed

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 = ( 78 + 97 ) / ( 316 + 312 )
p̂ = 0.2787
q̂ = 1 - p̂ = 0.7213
Z = ( 0.2468 - 0.3109) / √( 0.2787 * 0.7213 * (1/316 + 1/312) )
Z = -1.79

Test Criteria :-
Reject null hypothesis if Z < -Z(α/2)
Critical value Z(α/2) = Z(0.1/2) = 1.64 ( From Z table )
Z < -Z(α/2) = -1.79 < -1.64, hence we reject the null hypothesis
Conclusion :- We Reject H0

Conclusion :- ( does not ) appear to be enough evidence to support the claim that the proportion of online applications in 2009 was equal to than the proportion of online applications in 2003.

Critical value Z(α/2) = Z(0.1/2) = 1.64 ( From Z table )