Question

A research firm surveyed a sample of 300 individuals from a community and found out that 50 of them disagreed with a new construction project.

a) Use this sample to find the 95 % confidence interval estimate for the percentage of people in this community that would disagree with a new construction project in the community. Report the result using point estimate and margin of error.

b) At 5% level of significance, test to see the percentage of people who disagreed is less than 20%.

Answer 1

a)

Sample proportion = 50 / 300 = 0.167

Point estimate for p = 0.167

Margin of error = Z * sqrt ( ( 1 - ) / n)

= 1.96 * sqrt( 0.167 * 0.833 / 300)

= 0.042

95% CI is

- E < p < + E

0.167 - 0.042 < p < 0.167 + 0.042

0.125 < p < 0.209

95% CI is ( 0.125 , 0.209 )

b)

Since claimed proportion 20% lies in the confidence interval, we do not have sufficient evidence to

support the claim.