Question

For the data below construct a 95% confidence interval for the population mean.

53.4 51.6 48.0 49.8 52.8 51.8 48.8 43.4 48.2 51.8 54.6 53.8 54.6 49.6 47.2

Answer 1

Solution:

We are given a data of sample size n=15.

53.4,51.6,48.0,49.8,52.8,51.8,48.8,43.4,48.2,51.8,54.6,53.8,54.6,49.6,47.2

Using this, first we find sample mean() and sample standard deviation(s).

=   

=   

=   

= 50.6267

Now ,

s=   

Using given data, find Xi- for each term.take squre for each.then we can easily find s.

s= 3.1576

Confidence interval for population mean() using t distribution  

Given that,

= 50.6267 ....... Sample mean

s = 3.1576 ........Sample standard deviation

n = 15 ....... Sample size

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

Our aim is to construct 95% confidence interval.

c = 0.95

= 1- c = 1- 0.95 = 0.05

  /2 = 0.05 2 = 0.025

Also, n = 15

d.f= n-1 = 14

     =    = = 2.145

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

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

  

50.6267 - 2.145*(3.1576/ 15)    50.6267 + 2.145*(3.1576/ 15)

48.8779 < < 52.3755

is the required 95% confidence interval for mean....