Question

Suppose that the proportion of online shopping at Leon’s is 30%. If a given sample proportion is 0.80 and the sample size is 500, a 95% confidence interval would be Select one:

a. 0.80 ± 0.045. b. 0.80 ± 0.035. c. 0.80 ± 0.025. d. 0.80 ± 0.015

Answer 1

Solution :

Given that,

n = 500

Point estimate = sample proportion = = 0.80

1 - = 0.20

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )   

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

= 1.96 (((0.80*0.20) /500 )

= 0.035

A 95% confidence interval is ,

-+E

0.80+-0.035

b. 0.80 ± 0.035