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 145 freshmen students, 35 believed that the Big Bang theory accurately described the creation of planetary systems. Based on this information, s it correct at he α 0.05 evel 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 Ho:p=0.20 Ha p> 0.20 C. Ho: P 0.20 Ha: p <0.20 B. Ho:p#0.20 Ha : p = 0.20 D. Hop: 0.20 Ha: p #0.20 lf α = 0.05, find the rejection region for the test. Choose the correct answer below. OA. z>1.96 or z< -1.96 C.z>1.645 OE. Calculate the value of the test statistic. B. z< -1.96 0 D. z > 1.645 or z ← 1 .645 Z<-1.645 F. z> 1.96 (Round to two decimal places as needed.) z

Answer 1

H0: p = 0.2
Ha: p > 0.2

Here the significance level, 0.05. This is right tailed test; hence rejection region lies to the right.
Z(a) -
1.645 i.e. P(z > 1.645) = 0.05

This is right tailed test
Reject H0 if z > 1.645

pcap = 35/145 = 0.2414
n = 145

Test statistic,

z = (0.2414 - 0.2)/sqrt(0.2*0.8/145)
z = 1.25

P- P := V(p* (1 -p)/n

This is right tailed test
p-value = P(z > 1.25)
p-value = 0.1056

As test statistic < 1.645, fail to reject H0
There is not significant evidence to conclude that more than 20% students believe the BB therory decribes.