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 144 freshmen​ students,31believed that the Big Bang theory accurately described the creation of planetary systems. Based on this​information, is it correct at the α=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?

State the null and alternative hypotheses. Choose the correct answer below.

A.H0​:p=0.20 Ha​:p<0.20

B.H0​:p=0.20 Ha​:p≠0.20

C.H0​:p≠0.20 Ha​:p=0.20

D.H0​:p=0.20 Ha​:p>0.20

b. Calculate the value of the​ z-statistic for this test.

c. Calculate the​ p-value for this test.

d. What is the conclusion of the​ test?

Answer 1

a. Here claim is that more than​ 20% of all freshmen college students believe the Big Bang theory describes the creation of planetary​systems

So hypothesis is

D.H0​:p=0.20 Ha​:p>0.20

b. Now

Hence test statistics is

c. P value is

d. As P value is greater than alpha=0.1, we fail to test the null hypothesis

Hence there is not sufficient evidence to support the claim that p>0.20