Question

In: Statistics and Probability

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

The state test scores for 12 randomly selected high school seniors are shown on the right. Complete parts​ (a) through​ (c) below.

Assume the population is normally distributed.

12 scores-

1430

1220

985

694

729

837

724

750

544

621

1443

949

1) find the sample mean

2) find the standard deviation

3) construct a 90% confidence interval for the population mean

Solutions

Expert Solution


Solution :

Given that,

x x2
143 20449
1220 1488400
985 970225
694 481636
729 531441
837 700569
724 524176
750 562500
544 295936
621 385641
1443 2082249
949 900601
∑x=9639 ∑x2=8943823


Mean ˉx=∑xn

=143+1220+985+694+729+837+724+750+544+621+1443+949/12

=9639/12

=803.25

Sample Standard deviation S=√∑x2-(∑x)2nn-1

=√8943823-(9639)212/11

=√8943823-7742526.75/11

=√1201296.25/11

=√109208.75

=330.4675

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

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

t /2,df = t0.05,11=1.796

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

= 1.796 * (330.47 / 12 )

=171.32

Margin of error = 171.32

The 90% confidence interval estimate of the population mean is,

- E <  < + E

803.25 - 171.32 < < 803.25 + 171.32

631.92 < < 974.57

(631.92, 974.57 )

orchestra answered 1 year ago
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