Question

Jill comes to you and is interested in the mean calorie content of energy bars. She believes that the distribution of calorie content is approximately normal. You tell her to take a sample of energy bars. Jill comes back to you and says that she took a random sample of 12 energy bars, and found that, on average, there were 240 calories per bar, with a standard deviation of 30 calories. Use a 97% confidence interval?

Answer 1

Solution :

Given that,

= 240

s =30

n =12

Degrees of freedom = df = n - 1 =12 - 1 = 11

a ) At 97% confidence level the t is ,

= 1 - 97% = 1 - 0.97 = 0.03

  / 2= 0.03 / 2 = 0.015

t /2,df = t0.015,11 =2.491 ( using student t table)

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

= 2.491 * ( 30/ 12)

= 21.5727

The 97% confidence interval estimate of the population mean is,

- E < < + E

240 - 21.5727< < 240+ 21.5727

218.4273< < 261.5727

( 218.4273, 261.5727)