Question

7. A 95% confidence interval for the proportion of adults in Portland who have an iPhone is (0.303, 0.437). Find the number of people in the sample.7. A 95% confidence interval for the proportion of adults in BBC who have an iPhone is (0.303, 0.437). Find the number of people in the sample??

Answer 1

Solution :

Point estimate = = (Lower confidence interval + Upper confidence interval ) / 2

Point estimate = = (0.303 + 0.437) / 2

Point estimate = = 0.37

Margin of error = E = Upper confidence interval -

Margin of error = E = 0.437 - 0.37

Margin of error = E = 0.067

= 0.37

1 - = 1 - 0.37 = 0.63

margin of error = E = 0.067

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_0.025 = 1.96

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= (1.96 / 0.067)² * 0.37 * 0.63

= 855.78

sample size = n = 856