Question

A random sample of 6 cars from a particular model year had the following fuel consumption figures (in miles per gallon). Find the 99% confidence interval for the true mean fuel consumption for cars of this model year.

Sample data:

20.9, 18.1, 18.5, 21, 20.3, 20.2

find left endpoint & right endpoint.

Answer 1

Solution:

Given that,

x	dx	dx2
20.9	0.9	0.81
18.1	-1.9	3.61
18.5	-1.4	2.25
21	1	1
20.3	0.3	0.9
20.2	0.2	0.4
x = 119	dx = 1	dx2 = 7.8

a ) The sample mean is

Mean   = (x / n)

= (20.9 +18.1+ 18.5 + 21 + 20.3 + 20.2 / 6 )

= ( 119 / 6 )

= 19.33

Mean   = 19.3

b ) The sample standard is S

S = ( dx² ) - (( xd )² / n ) / 1 -n )

= (7.8 ( 1 )² / 6 ) / 5

   = (7.8 -0.1667 ) / 5

=7.6333 / 5

= 1.5267

= 1.2

The sample standard is = 1.2

= 19.3

s = 1.24

n = 25

Degrees of freedom = df = n - 1 = 6 - 1 = 5

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t _/2,df = t_0.005,5 = 4.031

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

= 4.031 * (1.2 / 6)

= 1.975

Margin of error = 1.975

The 99% confidence interval estimate of the population mean is,

- E < < + E

19.3 - 1.975< < 19.3 + 21.275

17.325 < < 21.275

left endpoint = 17.325

right endpoint = 21.275