Question

A Popeyes store manager wants a 90% confidence interval to estimate the proportion of customers who have tried their new chicken sandwich. She is also seeking a half-length of no more than 0.05 (B = 0.05). How many customers does the manager need to survey? (NOTE: Express the MULTIPLIER to three decimal places for your calculation.)

A 99

B 269

C 270

D 271

Answer 1

Solution :

Given that,

= 0.5 (assume 0.5)

1 - = 1 - 0.5 = 0.5

margin of error = E = 0.05

At 90% confidence level z

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table)

Sample size = n = (Z/2 / E)2 * * (1 - )

= (1.645 / 0.05)2 * 0.5 * 0.5

=271

Sample size = 271