Question

8) A researcher conducts a poll to study the level of educational attainment in a certain state. Of the 258 people surveyed by the researchers, 39 had a bachelor's Degree.

a) Find a 90% confidence interval for the true proportion of people the state with bachelor's degrees.

b) Provide the margin of error of the interval as your answer.

Round your answer to 4 decimal places.

Answer 1

Solution :

Given that,

n = 258

x = 39

Point estimate = sample proportion = = x / n = 39/258=0.151

1 - = 1-0.151=0.849

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645} ( Using z table )

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.645 (((0.151*0.849) /258 )

E= 0.0367

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.151 -0.0367< p < 0.151+0.0367

0.1143< p < 0.1877

The 90% confidence interval for the population proportion p is : 0.1143,0.1877