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.

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 = √(S^{2}/n)
Calculation
= 907.75
t = 2.2 Computed from table at degree of freedom of 11, ( DF=
n1)
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)
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