989 The state test scores for 12 randomly selected high school seniors are shown on the...

Solution:

x	x2
1424	2027776
695	483025
725	525625
623	388129
1221	1490841
721	519841
745	555025
1442	2079364
989	978121
837	700569
544	295936
947	896809
x=10913	x2=10941061

The sample mean is

Mean = (x / n) )

=1424+695+725+623+1221+721+745+1442+989+837+544+947 /12

=10913/12

=909.4167

Mean = 909.4

The sample standard is S

  S =( x2 ) - (( x)2 / n ) n -1

=10941061-(10913)212/11

=10941061-9924464.0833/11

=1016596.9167/11

=92417.90/15

=304.0031

The sample standard is =304.0

Degrees of freedom = df = n - 1 = 12 - 1 = 11

At 95% confidence level the t is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,11 =2.201

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

= 2.201 * (304.0 / 12)

= 193.1

Margin of error = 0.50

The 95% confidence interval estimate of the population mean is,

- E < < + E

909.4- 193.1 < < 909.4 + 193.1

716.2 < < 1102.5

(716.2, 1102.5)