Question

A random sample of 144 chicken nuggets in someone’s McDonalds order was observed. It is found that each nugget takes an average of 1.6 minutes to cook with a standard deviation of 1.3 minutes. Find a 95% confidence interval for the true mean time it takes to cook a nugget.

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 1.6

Population standard deviation =     = 1.3

Sample size n =144

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z / 2   = Z_0.025 = 1.96   ( Using z table )

Margin of error = E =   Z / 2     * ( /n)
= 1.96* (1.3 / 144 )

= 0.2123
At 95% confidence interval estimate of the population mean
is,

- E <   < + E

1.6 - 0.2123 <   < 1.6+ 0.2123

1.3877<   < 1.8123

( 1.3877,1.8123 )