Question

Researchers aim to study the weights of 10-year-old girls living in the United States (possibly to compare to other countries and thus compare growth rates). Based on previous studies, we can assume that weights of 10-year-old girls are Normal. From a small sample of 16 girls, the researchers find a sample average of ?̅ = 91.4 pounds and a sample standard deviation of ? = 2.8 pounds. Create a 99% confidence interval for the true average weight of 10-year-old girls in the U.S. (and make a formal conclusion based on your calculated interval).

Answer 1

Given that,

= 91.4

s =2.8

n = 16

Degrees of freedom = df = n - 1 =16 - 1 = 15

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2  df = t0.005,15 = 2.947 ( using student t table)

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

= 2.947 * ( 2.8/ 16) = 2.0629

The 99% confidence interval estimate of the population mean is,

- E < < + E

91.4- 2.0629< < 91.4+ 2.0629

89.3371 < < 93.4629

(89.3371 ,93.4629)