Question

According to National Surveys on basic scientific knowledge, 80% of high school students can correctly state that the Earth revolves around the Sun. But do they know how long it takes? Suppose the following question is included in the survey: How long does it take for the Earth to go around the Sun: one day, one month, or one year? 977 respondents out of 1,255 answered correctly.

Conduct a significance test to determine if the percentage of students who know how long it takes to go around the Sun is different from 80%.
In order to use the CLT to find the distribution of β, it's important to note that:

a) 1255 is greater than 30
b) Both 1,004 and 251 are greater than 10.
c) Both 977 and 1,255 are greater than 10.
d) Both 977 and 278 are greater than 10.
e) Both 1004 and 1255 are greater than 10.

Answer 1

b) Both 1,004 and 251 are greater than 10.

Explanation:

p = 0.80

n = 1255

In order to use CLT the distribution of
`\hat{p}` should have np and n(1-p) greater than 10.

np = 1255*0.80

np = 1004

n(1-p) = 1255*0.20

n(1-p) = 251.00

Since Both 1004 and 251 are greater than 10,