Question

In 2015, 19.9% of all Bachelor's degrees were awarded to women. The administration at UC decided to see whether female enrollment differed significantly from the national average, so they took a random sample of 80 engineering students and found that 13 of them were female.

A) Identify and calculate the appropriate test statistic for this experiment.

B) set up a hypothesis test for this experiment

C) Is this sample sufficiently large? Why?

D) What is the standard deviation of the sampling distribution?

E) For a significance level of a=0.1, identify the rejection region for this experiment. (sketch as well as explain)

F) What is the appropriate conclusion of this hypothesis test?

Answer 1

Part a)

P = X / n = 13/80 = 0.1625

Test Statistic :-
Z = ( P - P0 ) / ( √((P0 * q0)/n)
Z = ( 0.1625 - 0.199 ) / ( √(( 0.199 * 0.801) /80))
Z = -0.8177

Part b)

H0 :- P = 0.199
H1 :- P ≠ 0.199

Part c)

Condition check for Normal Approximation to Binomial
n * P >= 10 = 80 * 0.1625 = 13
n * (1 - P ) >= 10 = 80 * ( 1 - 0.1625 ) = 67

Yes, sample size is sufficiently large

Part d)

Standard deviation = = 0.041245

Part e)

Test Criteria :-
Reject null hypothesis if Z < -Z(α/2)
Z(α/2) = Z(0.1/2) = 1.645
Z > -Z(α/2) = -0.8177 > -1.645, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Part f)

Conclusion :- We Fail to Reject H0

There is insufficient evidence to support the claim that  female enrollment differed significantly from the national average.