Question

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?

Answer 1

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.

Step-by-step 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.