Question

A survey was conducted to estimate the proportion of car drivers who use seatbelts while driving. Of the 1500 drivers sampled, 520 drivers said, they always use a seatbelt while driving. The same study of charity contributions revealed that 20 of the 50 families sampled do charity regularly.

1. Should the finite-population correction factor be used? Why or why not?
2. Construct the 95 percent confidence interval for the proportion of families doing charity regularly.

Answer 1

Answer)

1)

No as the finite-population correction factor is used when we sample more than 5% of the finite population.

Here we do not have the finite population.

2)

N = 50

P = 20/50

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 20

N*(1-p) = 30

Both the conditions are met so we can use standard normal z table to estimate the interval

Critical value z from z table for 95% confidence level is 1.96

Margin of error (MOE) = Z*√p*(1-p)/√n

P = 20/50

N = 50

Z = 1.96

MOE = 0.13579278331

Confidence interval is given by

(P-MOE) < P < (P+MOE)

0.26420721668 < P < 0.53579278331