Question

Traditionally 18% of undergraduates in the U.S. major in business. A recent sample of 863 undergraduates found 21% major in business. Perform a hypothesis test to see if the percentage of undergraduates majoring in business has significantly increased from past norms

A. What is H_o ?

B. What is H₁?

C. Assuming α = 2.5%, what is the test statistic for this hypothesis test?

D. Assuming α = 2.5%, what is the critical value for this hypothesis test?

E. What is the conclusion to this hypothesis test for α = 2.5%?

F. Assuming α = 1%, what would be the conclusion to this hypothesis test?

Answer 1

Below are the null and alternative Hypothesis,
a)

Null Hypothesis, H0: p = 0.18

b)

Alternative Hypothesis, Ha: p > 0.18

c)

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.21 - 0.18)/sqrt(0.18*(1-0.18)/863)
z = 2.29

d)
Rejection Region
This is right tailed test, for α = 0.025
Critical value of z is 1.96.
Hence reject H0 if z > 1.96

e)

reject the null hypothesis.

f)

This is right tailed test, for α = 0.01
Critical value of z is 2.33.
Hence reject H0 if z > 2.33

fail to reject the null hypothesis.