Question

A simple random sample of 16 students from our class was taken. The mean height was 66.9 inches with a standard deviation of 2.8 inches. You will be asked some questions about confidence intervals for the actual mean height of all the students in this class.

Interpret the 99% confidence interval.

Answer 1

)solution

Given that,

= 66.9

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) = 2.06

The 99% confidence interval is,

- E < < + E

66.9 - 2.06 < < 66.9+ 2.06

64.84 < < 68.96