Question

According to 2017 US Census data, 23% of Kentucky adults age 25 and older have a bachelor’s degree or higher. You suspect that percentage has decreased. You find in a random sample of 900 Kentuckians age 25 and older that 199 have a bachelor’s degree. Use this prompt for the next five questions to conduct a hypothesis test at the α=0.05 significance level to determine if the percent of Kentuckians with a college degree has decreased since 2017.

a) State the hypotheses.

b) Calculate the sample proportion. Round to four decimal places

c) Calculate the test statistic. Only enter the numeric value of the test statistic (not "z=" or "t="), rounded to two decimal places. If it is negative, include the negative sign

d) Calculate the p-value. Round to two decimal places

e) State the conclusion of the hypothesis test.

		Fail to reject the null hypothesis. We do not have enough evidence to conclude the the proportion of Kentuckians with a college degree has decreased since 2017.
		Accept the null hypothesis. The proportion of Kentuckians with a college degree has not decreased since 2017.
		Reject the null hypothesis. The proportion of Kentuckians with a college degree has decreased since 2017.
		Fail to reject the null hypothesis. The proportion of Kentuckians with a college degree has decreased since 2017

Answer 1

a)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.23
Alternative Hypothesis, Ha: p < 0.23

b)

sample proportion = 199/900 = 0.2211

c)

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.2211 - 0.23)/sqrt(0.23*(1-0.23)/900)
z = -0.63

d)

P-value Approach
P-value = 0.26

e)

As P-value >= 0.05, fail to reject null hypothesis.

Fail to reject the null hypothesis. We do not have enough evidence to conclude the the proportion of Kentuckians with a college degree has decreased since 2017.