Question

A university's Office of Admission document claims that 54.9% of that university's undergraduates are female. To test this claim, a random sample of 200 undergraduates was selected. In this sample, 47.8% were female.  

A) Is there sufficient evidence to conclude that the document's claim is false?

B) Carry out a hypothesis test at a 10% significance level.

C) Find the value of the standardized test statistic, the positive critical value, the negative critical value, and the p-value

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.549
Alternative Hypothesis, Ha: p ≠ 0.549

Rejection Region
This is two tailed test, for α = 0.1
Critical value of z are -1.645 and 1.645.
Hence reject H0 if z < -1.645 or z > 1.645

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.478 - 0.549)/sqrt(0.549*(1-0.549)/200)
z = -2

P-value Approach
P-value = 0.0455
As P-value < 0.1, reject the null hypothesis.
there is  sufficient evidence to conclude that the document's claim is false