A professor wished to study whether the percentage of Americans that graduate from college has increased. Ten years, ago, 25% of Americans graduated from college. This year, a random sample had a college graduation rate of 28%. When the professor calculated her hypothesis test at significance level 0.05, she obtained a p-value of 0.21. What should she conclude?

There is not sufficient evidence to conclude that the percentage of Americans that graduate from college has increased at the 0.05 level of significance.

Explanation:

Sample size, n = not given

Sample Proportion, P = 25%

Hypothesized proportion, P = 28%

p-value = 0.21

The level of significance = α = 0.05

Null hypothesis, H0: P = 28

Alternative hypothesis, Ha: P >28

To determine whether to reject or accept, we would use the decision rule:

If p-value is less than or equal to level of significance, reject the null hypothesis.

If p-value is not less than or not equal to level of significance, do not reject the null hypothesis.

Since p-value is greater than level of significance, we would accept the null hypothesis.

0.21 < 0.05

Conclusion:

There is not sufficient evidence to conclude that the percentage of Americans that graduate from college has increased at the 0.05 level of significance.