Question

A sample of size =n47 has sample mean =x57.6 and sample standard deviation =s9.5. Part: 0 / 20 of 2 Parts Complete Part 1 of 2 Construct a 99.5% confidence interval for the population mean μ. Round the answers to one decimal place. A 99.5% confidence interval for the population mean μ is <<μ .

Answer 1

Solution:

Given that,

   = 57.6

s = 9.5

n = 47   

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

Our aim is to construct 99.5% confidence interval.   

c = 0.995

= 1- c = 1- 0.995 = 0.005

  /2 = 0.10 2 = 0.0025

Also, d.f = n - 1 = 47 - 1 = 46  

    =    =  _0.05,46 = 2.949

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

The margin of error is given by

E =  /2,d.f. * ( / n)

= 2.949 * (9.5 / 47)

= 4.1

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

( - E ) <   <  ( + E)

(57.6 - 4.1)   <   <  (57.6 + 4.1)

53.5 <   < 61.7

. A 99.5% confidence interval for the population mean μ is  53.5 <   < 61.7