Question

If n=19, ¯xx¯=34, and s=5, construct a confidence interval at a 80% confidence level. Assume the data came from a normally distributed population.

Give your answers to one decimal place.

Enter answer in interval notation

(____,____)

Answer 1

Solution :

Given that,

= 34

s =5

n = 19

Degrees of freedom = df = n - 1 =19 - 1 = 18

At 80% confidence level the t is ,

= 1 - 80% = 1 - 0.80 = 0.20

  / 2= 0.20 / 2 = 0.10

t /2,df = t0.10,18 = 1.330 ( using student t table)

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

= 1.330 * ( 5/ 19)

= 1.5

The 80% confidence interval is,

- E < < + E

34 - 1.5 < < 34+ 1.5

32.5 < < 35.5

(32.5,35.5 )