Question

A marketing research company hired by Pepsi is interested in estimating the proportion of cola customers in Ontario who prefer Pepsi to other brands. A simple random sample of 120 Ontario cola customers was selected and 45% of them reported favoring other brands over Pepsi.

What is the upper limit of the large sample 95% confidence interval for the true proportion of cola customers in Ontario who prefer Pepsi to other brands?

(Hint – use 6 decimal places for intermediate calculations to avoid too much rounding error.)

• A. 0.639

• B. 0.089

• C. 0.088

• D. 0.636

• E. 0.539

Answer 1

Solution :

Given that,

n = 120

Point estimate = sample proportion = =45% = 0.45

1 - = 1- 0.45 = 0.55

Z_/2 = 1.960

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

= 1.960 * ((0.45*(0.55) /120 )

= 0.089

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.450- 0.089 < p < 0.450+0.089

0.361< p < 0.539

The 95% confidence interval for the population proportion p is : 0.361,0.539

Upper limit = 0.539

E. 0.539