Question

10)

The SAT scores for 12 randomly selected seniors at a particular high school are given below. Assume that the SAT scores for seniors at this high school are normally distributed.

1,271	1,288	1,278	616	1,072	944
1,048	968	931	990	891	849

a) Find a 95% confidence interval for the true mean SAT score for students at this high school.

b) Provide the right endpoint of the interval as your answer.

Round your answer to the nearest whole number.

Answer 1

Solution:

x	x2
1271	1615441
1288	1658944
1278	1633284
616	379456
1072	1149184
944	891136
1048	1098304
968	937024
931	866761
990	980100
891	793881
849	720801
x=12146	x2=12724316

The sample mean is

Mean = (x / n) )

=1271+1288+1278+616+1072+944+1048+968+931+990+891+849/12

=12146/12

=1012.1667

The sample standard is S

  S =( x² ) - (( x)² / n ) n -1

=√12724316-(12146)²12/11

=√12724316-12293776.3333 /11

=√430539.6667/11

=√39139.9697

=197.8382

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 = t_0.025,11 =2.201

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

= 2.201 * (198 / 12)

= 125.80

Margin of error = 125.80

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

- E < < + E

1012 -125.80 < < 1012 + 125.80

886.20 < < 1137.80

b) The right endpoint =1138