Question

A random sample of 18 Belgium chocolate bars has, on average, 345 calories per bar, with a standard deviation of 28 calories.  Construct a 95% confidence interval for the true mean calorie content of these chocolate bars.  Assume that the distribution of the calorie content is approximately normal

Answer 1

Solution :

Given that,

= 345

s =28

n =18

Degrees of freedom = df = n - 1 = 18- 1 = 17

a ) At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,17 =2.110 ( using student t table)

Margin of error = E = t/2,df * (s /n)

=2.110 * (28 / 18)

= 13.9253

The 95% confidence interval estimate of the population mean is,

- E < < + E

345 -13.9253 < < 345+ 13.9253

331.0747 < < 358.9253

( 331.0747 ,358.9253)