Question

6. The owner of the West End Kwick Fill Gas Station is interested in installing a pay-at-the-pump system, and wants to know the proportion of customers who would use it. He surveys100 customers and finds that 80 would like to pay at the pump.(a) Estimate the value of the sample proportion.(b) Compute the standard error of the population.(c) Develop a 90% confidence interval for the population proportion.(d) Interpret your findings for the owner.

Answer 1

Solution :

Given that,

n =100

x = 80

(a)

Point estimate = sample proportion = = x / n = 80/100=0.8

1 - = 1-0.8=0.2

(b)

standard error = (( * (1 - )) / n)

=(((0.8*0.2) /100 )

= 0.04

(c)

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

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

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

= 1.645 (((0.8*0.2) /100 )

= 0.0658

=0.1 (rounded)

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.8-0.1 < p < 0.8+0.1

0.7< p < 0.9

(d)

The 90% confidence interval for the population proportion p is : (0.7 ,0.9)

lower bound 0.7

upper bound 0.9