Module 8 examples - Statistical Inference

Estimation Sample

49 light bulbs last average 1100 hours the standard distribution is 70

sample size (n) = 49

SD = 70

Sample SD = 70 / = 70/7 = 10

Mean = = 1100

95% confidence

=

= 1100 (70)/

= 1100 (70)/ 7

= 1100 (10)

= 1100 20

95% confidence 1080 - 1120

Calculate Sample size

Instead of sample size being known and the confidence limits unknown the situation is reversed at the 95 % confidence level

light bulbs last average 1100 hours the standard distribution is 70 5 hours ( with 95% confidence)

-Confidence limits required = x +/- 2 (SD) /

1100 5 hours

1100 5 hours = 1100 2(70) /

1100 –1100 5 = 1100 – 1100 140 /

5 = 140 /

+ 5-5 = 140 /5

= 140/5

= 28

n =

n = 784

For a binomial distribution the standard deviation is:

Where p is the parameter. In this case,

SD = = 0.05