Question

1. Construct 95% confidence intervals for
   1. the population variance and
   2. population standard deviation of the given values below
   3. Sketch the results and interpret your findings (15 points).

1.286   1.138   1.240   1.132   1.381   1.137

1.300   1.167   1.240   1.401   1.241   1.171

1.217   1.360   1.302   1.331   1.383

Answer 1

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Answer:

The given data: 1.286,1.138,1.240,1.132,1.381,1.137,1.300,1.167,1.240,1.401,1.241,1.171,1.217,1.360,1.302,1.331,1.383

x	x²
1.286	1.6538
1.138	1.295
1.24	1.5376
1.132	1.2814
1.381	1.9072
1.137	1.2928
1.3	1.69
1.167	1.3619
1.24	1.5376
1.401	1.9628
1.241	1.5401
1.171	1.3712
1.217	1.4811
1.36	1.8496
1.302	1.6952
1.331	1.7716
1.383	1.9127
∑x = 21.427	∑x² = 27.1415

Mean:

x¯ = ∑x / n

     = 21.427 / 17

x¯ = 1.2604

a)

Population Variance:

σ² = [ ∑x² - (∑x)² / n ] / n

= [ 27.1415 - (21.427)² /17 ] / 17

= [ 27.1415 - 27.0068 ] / 17

= 0.1347 / 17

σ² = 0.0079

b)

Population Standard deviation σ:

σ = √0.0079

σ = 0.089

c)

Frequency Distribution Table
Class	Frequency	Percentage
1.1 - 1.179	5	29.50%
1.18 - 1.259	4	23.50%
1.26 - 1.339	4	23.50%
1.34 - 1.419	4	23.50%
Total	17	100.00%