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.a. P-value = 0.816, fail to reject the null hypothesisb. P-value = 0.184, fail to reject the null hypothesisc. P-value = 0.368, fail to reject the alternative hypothesisd. P-value = 0.816, reject the null hypothesise. P-value = 0.184, fail to reject the alternative hypothesisf. P-value = 0.368, fail to reject the alternative hypothesis

Answer 1

Answer:

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

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 1426

p = 0.5

Alpha, α = 0.10

Number of students who earned bachelor's degrees within 5 years, x = 696

First, we design the null and the alternate hypothesis  

$H_{0}: p \geq 0.5\\H_A: p < 0.5$

This is a one-tailed(left) test.  

Formula:

$\hat{p} = \dfrac{x}{n} = \dfrac{696}{1426} = 0.488$

$z = \dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}$

Putting the values, we get,

$z = \displaystyle\frac{0.488-0.5}{\sqrt{\frac{0.5(1-0.5)}{1426}}} = -0.90$

Now, we calculate the p-value from the table.

P-value = 0.184

Since the p-value is greater than the significance level, we fail to reject the null hypothesis and accept the null hypothesis.

Thus, there is not enough evidence to support the claim that  that at least half of college students earn bachelor's degrees within 5 years.

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