Answer to Question #125505 in Statistics and Probability for jse

Question

An article in Fortune (September 21, 1992) claimed that nearly one-half of all engineers continue academic studies beyond the B.S. degree, ultimately receiving either an M.S. or a Ph.D. degree. Data from an article in Engineering Horizons (Spring 1990) indicate that 117 of 484 new engineering graduates were planning graduate study.

1. Test the hypothesis H0 : p=0.5 versus H1: p is not equal to 0.5. Usea a = 0.05

A. Fail to reject H0
B. Reject H0

2. What is the P-value for this test? Round your answer to 4 decimal places. Enter your answer in accordance to the question statement

Answer 1

Solution:

The following information is provided: The sample size is N = 484

the number of favorable cases is X = 117 and the sample proportion is $\bar p = \frac{X}{N} = \frac{ 117}{ 484} = 0.2417$ and the significance level is α=0.05.

The following null and alternative hypotheses need to be tested:

$Ho: p = 0.5 Ha: p \neq ​ 0.5$

This corresponds to a two-tailed test, for which a z-test for one population proportion needs to be used.

$z = \frac{\bar p - p_0}{\sqrt{p_0(1-p_0)/n}} = \frac{ 0.2417 - 0.5 }{\sqrt{ 0.5(1- 0.5)/484}} = -11.364$

Using the P-value approach:Using Z table find the value left to -11.36

P value= 2(1- invnorm(11.36))=0.

The p-value is p = 0 and since p=0<0.05, it is concluded that the null hypothesis is rejected.

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population proportion p is different than p0 at α=0.05 significance level.