Question

A simple random sample is conducted of 1426 college students who are seeking bachelor's degrees, and it includes 696 who earned bachelor's degrees within 5 years. Use a 0.10 significance level to test the claim that at least half of college students earn bachelor's degrees within 5 years. Use P-value method and determine conclusion.

Select one:

a. P-value = 0.816, fail to reject the null hypothesis

b. P-value = 0.184, fail to reject the null hypothesis

c. P-value = 0.368, fail to reject the alternative hypothesis

d. P-value = 0.816, reject the null hypothesis

e. P-value = 0.184, fail to reject the alternative hypothesis

f. P-value = 0.368, fail to reject the alternative hypothesis

Answer 1

H0: Null hypothesis: P = 0.5

HA: Alternative hypothesis: P > 0.5

n = sample size = 1426

p = sample proportion = 696/1426 = 0.4881

P = Population proportion = 0.5

Q = 1 - P = 0.5

The test statistic is:

Z = (p - P)/SE

= (0.4881 - 0.5)/0.0132 = - 0.9031

One tail - Right side test

Table of Area Under Standard Normal Curve gives area = 0.3159

So,

P value = 0.5 + 0.3159= 0.8159

= 0.10

Since P value = 0.8159 is greater than = 0.10, H0 is accepted.

So,

Correct option:

a. P-value = 0.816, fail to reject the null hypothesis.