Sociologists say the percentage of the classic music lovers is about 5%. From the survey, we know that only 83 out of 2000 people listen to the classic music. Let denote the proportion of the classic music lovers. The hypotheses are H0: p=0.05 vs Ha: p≠0.05. The p-value for this two-tailed test based on the normal distribution is 0.09. What is the p-value for a chi-square test?

Given that sociologists say the percentage of the classic music lovers is about 5%. From the survey, we know that only 83 out of 2000 people listen to the classic music. Let denote the proportion of the classic music lovers. The hypotheses are H0: p=0.05 vs Ha: p≠0.05

p value = 0.09

Instead of this if we do chi square

H0: Proportion of music lovers is 5% and non music lovers is 95%

Ha: Proportions are not as per the estimate

(Two tailed chi square test)

Observed 83 1917 2000

Expected 100 1900 2000

O-E -17 17 0

chi square

(O-E)^2/E 2.89 0.1521 3.0421

df =1

p value from chi square = 0.081

Though p value is not exactly the same, the conclusion in both tests are the same