Question

In: Statistics and Probability

1. 120 142 158 128 135 152 Find x̅, s, and t. construct a 90% confidence...

1. 120 142 158 128 135 152

Find x̅, s, and t. construct a 90% confidence interval of the population mean.

Expert Solution

Solution

Given that

x	x2
120	14400
142	20164
158	24964
128	16384
135	18225
152	23104
∑x=835	∑x2=117241

Mean ˉx=∑xn

=120+142+158+128+135+152/6

=835/6

=139.1667

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

=√117241-(835)26/5

=√117241-116204.1667/5

=√1036.8333/5

=√207.3667

=14.4002

Degrees of freedom = df = n - 1 = 6 - 1 = 5

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

t_/2,df = t_0.05,5 =2.015

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

= 2.015 * (14.40 / $\sqrt$ 6)

= 11.85

Margin of error = 11.85

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

- E < < + E

139.17 - 11.85 < < 139.17 + 11.85

127.32 < < 151.02

(127.32, 151.02 )

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