Question

30.   POPT Popcorn is trying to determine the proportion of popcorn kernels used that will pop, with the maximum error
of 2.5%. How many kernels must be sampled to meet this requirement at the 90% confidence level if there is a
preliminary estimate of is 34%?

A. 1537

B. 15

C. 1083

D. 972

31.  In a marketing survey, a random sample of 800 shoppers revealed that 625 remained loyal to their favorite
supermarkets during the past year. Find a 99% confidence interval for the percentage of people who will remain
loyal to their supermarket.   

A. 0.72 < p < 0.79

B. 0.74 < p < 0.82

C. 0.87 < p < 0.98

D. 0.77 < p < 0.85

Answer 1

30)

Solution :

Given that,

= 0.34

1 - = 0.66

margin of error = E = 0.025

Z_/2 = 1.645

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

= (1.645 / 0.025)² * 0.34 * 0.66

= 972

sample size = n = 972

31)

Point estimate = sample proportion = = x / n = 800 / 625 = 0.781

Z_/2 = 2.576

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

= 2.576* (((0.781 * 0.219) / 800)

= 0.037

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.781 - 0.037 < p < 0.781 + 0.037

0.74 < p < 0.82