Question

2 - A random sample of n = 12 values taken from a normally distributed population resulted in the sample values below. Use the sample information to construct a 98% confidence interval estimate for the population mean.

105 111 95 106 114 108 114 111 105 113 113 95

Answer 1

Solution :

Given that,

x	x2
105	11025
111	12321
95	9025
106	11236
114	12996
108	11664
114	12996
111	12321
105	11025
113	12769
113	12769
95	9025
∑x=1290	∑x2=139172

Mean ˉx=∑xn

=105+111+95+106+114+108+114+111+105+113+113+95/12

=1290/12

=107.5

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

=√139172-(1290)212/11

=√139172-138675/11

=√497/11

=√45.1818

=6.7217

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

At 98% confidence level the t is ,

= 1 - 98% = 1 - 0.98= 0.02

/ 2 = 0.021 / 2 = 0.01

t _/2,df = t_0.01,11 =2.718

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

= 2.718 * (6.72 / 12)

= 5.27

Margin of error = 5.27

The 98% confidence interval estimate of the population mean is,

- E <  < + E

107.5 - 5.27 < < 107.5 + 5.27

102.23 < < 112.77

(102.23, 112.77 )