Question

The owner of the West End Kwick Fill Gas Station wishes to determine the propor- tion of customers who pay at the pump using a credit card or debit card. He surveys 100 customers and finds that 80 paid at the pump.

a) point estimate=

b)standard error of the proportion (rounf 2 decimals)

c) critical valur for 95% =+-

d) Margin of error (2 decimals)

e) Lower and uppef limit of confidence interval= (2decimals)

Answer 1

Solution =     

Given,

n = 100 ....... Sample size

x = 80 .......no. of successes in the sample

Let denotes the sample proportion.

     = x/n   = 80 / 100 = 0.80  

Standard error of the proportion,

SE = = 0.80(1 - 0.80) /100 = 0.04

Our aim is to construct 95% confidence interval.

c = 0.95

= 1- c = 1- 0.95 = 0.05

  /2 = 0.025 and 1- /2 = 0.975

Search the probability 0.975 in the Z table and see corresponding z value

= 1.96

Now , the margin of error is given by

E = /2 *  

= 1.96 * [ 0.80 *(1 - 0.80)/ 100]

= 0.08

Now the confidence interval is given by

( - E)   ( + E)

( 0.80 - 0.08)   ( 0.80 + 0.08 )

0.72   0.88  

Required 95% Confidence Interval is ( 0.72 , 0.88 )

a) point estimate = 0.80

b)standard error of the proportion = 0.04

c) critical valur for 95% = 1.96

d) Margin of error = 0.08

e) Lower and uppef limit of confidence interval = 0.72 , 0.88