Question

1. A study at State University was to determine student opinions regarding non-revenue-generating athletics. Specifically, one question in a survey asked students "Do you think that the women's basketball program should be discontinued?" The data collected revealed that 350 of the 1,000 females surveyed (sample 1) responded "Yes" and 400 of the 1,000 males surveyed (sample 2) responded "Yes." Test if the proportion of females who agree to discontinue women’s basketball program is lower than the proportion among males. Use a 0.05 level of significance.

What hypothesis test should be used?

Test for two proportions

Independent samples z-test

Independent samples t-test

Matched pairs t-test

2. State the null and alternative hypotheses.

H0: mu1=mu2, Ha: mu1<mu2

H0: p1=p2, Ha: p1 not = p2

H0: p1=p2, Ha: p1<p2

H0: p1=p2, Ha: p1>p2

3. Find the value of test statistic.

2.31

-2.31

2.58

-2.58

4. Find the p-value.

0.0208

0.4896

0.9792

0.0104

5. What is your decision, reject H₀ or not?

Reject H0, because p-value < alpha

Reject H0, because p-value > alpha

Do not reject H0, because p-value > alpha

Do not reject H0, because p-value < alpha

6. Interpret the conclusion in the context of the problem. At 0.05 level of significance, …

There is not sufficient evidence that the proportion of females who agree to discontinue women’s basketball program is equal than the proportion of males.

There is sufficient evidence that the proportion of females who agree to discontinue women’s basketball program is equal than the proportion of males.

There is not sufficient evidence that the proportion of females who agree to discontinue women’s basketball program is lower than the proportion of males.

There is sufficient evidence that the proportion of females who agree to discontinue women’s basketball program is lower than the proportion of males.

Answer 1

p1cap = X1/N1 = 350/1000 = 0.35
p1cap = X2/N2 = 400/1000 = 0.4
pcap = (X1 + X2)/(N1 + N2) = (350+400)/(1000+1000) = 0.375

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 < p2

Test for two proportions

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.35-0.4)/sqrt(0.375*(1-0.375)*(1/1000 + 1/1000))
z = -2.31

P-value Approach
P-value = 0.0104

As P-value < 0.05, reject the null hypothesis.
Reject H0, because p-value < alpha

There is sufficient evidence that the proportion of females who agree to discontinue women’s basketball program is lower than the proportion of males.