Question

A utility company sampled 400 customers and finds that 146 of them had a discrepancy on their service bill. What is the upper bound for the 99% confidence interval for the proportion of customers with discrepancies on their service bill. Round 2 three decimal places

Answer 1

Solution :

Given that,

n = 400

x = 146

Point estimate = sample proportion = = x / n =146/400=0.365

1 - = 1-0.365=0.635

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

= 0.01

Z_/2 = Z_0.01 = 2.326 ( Using z table )

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

= 2.326 (((0.365*0.635) /400 )

E = 0.06

A 99% confidence interval for population proportion p is ,

+ E

0.365+0.06

0.425

upper limit=0.425