Question

A group of professors investigated​ first-year college​ students' knowledge of astronomy. One concept of interest was the Big Bang theory of the creation of the universe. In a sample of 148 freshmen​ students, 34 believed that the Big Bang theory accurately described the creation of planetary systems. Based on this​ information, is it correct at the alpha=0.10 level of significance to state that more than​ 20% of all freshmen college students believe the Big Bang theory describes the creation of planetary​ systems?

1. state the null and hypotheses

2. if alpha=0.10, find the rejection region for this test

3. calculate the value of the test statistic (round to two decimal places)

4. make the appropriate conclusion. choose the correct answer below

a. Fail to reject H0 - enough evidence

b. Fail to reject H0 - not enough evidence

c. reject H0 - enough evidence

d. reject H0 - not enough evidence

Answer 1

Ans1:

H0 : p = 0.30
Ha: p > 0.30

Ans2>

This is a right tailed test

Critical value : 1.282

Reject H0 if z >1.282

Ans3.

test statistics:

phat = 34/148 = 0.229

z = (phat -p)/sqrt(p*(1-p)/n)
= (0.229 - 0.30)/sqrt(0.20*(1-0.30)/148)
=- 1.865

z=-1.87

p value = 1 - P(z< 1.865)
= 1 - 0.0310
p value = 0.9689

Do not reject H0 as p value > 0.1 significance level

Ans4>

Concusion:.

b. Fail to reject H0 - not enough evidence