Question

An Office of Admission document at a certain university claims that 56.1% of their undergraduates are female. To test this claim, a random sample of 230 undergraduates was selected. In this sample, 58.1% were female. Is there sufficient evidence to conclude that the document's claim is false? Carry out a hypothesis test at a 10% significance level.

A. The value of the test statistic is:

B. The p-value is

D. Your decision for the hypothesis test:

A. Reject H0.
B. Do Not Reject H0.
C. Reject H1.
D. Do Not Reject H1.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H0 : p =0.561

Ha : p 0.561

n = 230

= 0.581

P0 = 0.561

1 - P0 = 1 - 0.561 = 0.439

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.581-0.561/ [(00.561*0.439) / 230 ]

= 0.61

Test statistic = z = 0.61

P(z >0.61 ) = 1 - P(z < 0.61 ) =1 - 0.7291

P-value = 2 * 0.2709 =0.5418

= 0.010

P-value <>

0.5418 > 0.10

Fail to reject the null hypothesis .

There is not sufficient evidence to suggest that