Question

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.

1425

1223

988

694

720

830

721

743

544

620

1442

943

​(a)Find the sample mean.

x=____

​(Round to one decimal place as​ needed.)

​(b) Find the sample standard deviation.

s=____ (Round to one decimal place as​ needed.)

​(c) Construct a

95%

confidence interval for the population mean

μ.

A

95%

confidence interval for the population mean is

​(_,_).

​(Round to one decimal place as​ needed.)

Answer 1

Given sample as

1425
1223
988
694
720
830
721
743
544
620
1442
943

Hence according to question

a) Mean of the data can be found by

Hence mean =907.8

b) Sample Standard deviation calculated as

Hence Sample standard deviation as 305.1

c) 95% Confidence interval calculated as

The formula for estimation is:

μ = ± t *(S_m)

where:

= sample mean
t = t statistic determined by confidence level
S_m = standard error = √(S²/n)

Calculation

= 907.75
t = 2.2 Computed from table at degree of freedom of 11, ( DF= n-1)
S_m = √(301.1312/12) = 86.93

μ = ± t*(S_M)
μ = 907.75 ± 2.2*86.93
μ = 907.75 ± 191.3295

Hence Confidence interval as

(716.4 and 1099.1)