Question

Q. A researcher wanted to estimate the true proportion of smokers in a certain city (?). He selected a random sample of size ? = 50 people and found 15 smokers in the sample.

a) Find a point estimate for (?).

b) Find a 95% confidence interval for (?).

c) If we use the sample proportion (?̅) to estimate (?), calculate the margin of error using the confidence level 0.95.

Answer 1

Given. n=50 x=15

sample proportion=x/n =15/50 = ?̅

a. point estimate (?) = 15/50

= 0.3 Answer

b. 95% confidence interval for (?)

?̅ z0.05 *standatrd error of ( ?̅ )

0.3 1.96*?̅ (1-?̅)/n

   0.3 1.96* 0.3*0.7/50

  0.3    1.96* (0.064807407)

0.30.127022518

{0.17298, 0.427023 } Answer

c. Margin of error = 1.96*?̅ (1-?̅)/n

= 0.127022518 Answer