Question

The following random sample was selected from a normal distribution 3.5, 5.4, 1.3, 1.8, 4.3 then the 95% confidence interval to estimate the population of the mean.

I am having a tough time calculating I feel I just need an idea how to calculate this type of scenario homework properly.

Answer 1

Solution:

We are given a data of sample size n = 5

3.5, 5.4, 1.3, 1.8, 4.3

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

=   

= (3.5 + 5.4.+ 1.3 + 1.8 + 4.3)/5

= 3.26

Now ,

s=   

Using given data, find Xi - for each term.Take square for each.Then we can easily find s.

s= 1.70967833   

( We can directly find s using calculators)

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 = 5

d.f = n-1 = 4

     =    = = 2.776

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

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

  

3.26 - 2.776*(1.70967833/ 5)     3.26 + 2.776*(1.70967833/ 5)

3.26 − 2.123 <   <  3.26 + 2.123

1.137 <   < 5.383

Answer : The required 95% interval is (1.137 , 5.383)