Question

Construct the indicated confidence interval for the population mean u using​ (a) a​ t-distribution. (b) If you had incorrectly used a normal​ distribution, which interval would be​ wider?

c=0.99​, x =14.2​, s=4.0​, n=8

(a) The 99​% confidence interval using a​ t-distribution is ( _, _ )

Answer 1

Solution:

Confidence interval for population mean() using t distribution  

Given that,

= 14.2 ....... Sample mean

s = 4.0 ........Sample standard deviation

n = 8 ....... Sample size

Note that, Population standard deviation() is unknown..So we use t distribution.

Our aim is to construct 99% confidence interval.

c = 0.99

= 1- c = 1- 0.99 = 0.01

  /2 = 0.01 2 = 0.005

Also, n = 8

d.f= n-1 = 7

     =    = = 3.499 (using t table)

( use t table or t calculator to find this value..)

Now , confidence interval for mean() is given by:

  

14.2 - 3.499*(4.0/ 8)   14.2 + 3.499*(4.0/ 8)

14.2 - 4.949     14.2 + 4.949

9.251   19.149

Answer is (9.251 , 19.149)