A machine used for packaging seedless golden raisins is set so that their standard deviation in the weight of raisins packaged per box is 0.25 ounce. The operations manager wishes to test the machine setting and selects a sample of 30 consecutive raisin packages filled during the production process.

Question

Weights
15.2
15
14.3
15.3
15.2
14.4
15.1
15.4
15.5
15.7
15.6
15.4
15.3
15.7
15.2
15
15.4
15.5
15.1
15.3
15.6
14.3
14.9
15.1
14.6
14.8
15.3
14.5
14.6
15.1

At the 0.05 level of significance, is there evidence that the population standard deviation differs from 0.25 ounces?
What assumptions are made in order to perform this test?

Answer 1

First establish a null hypothesis
H0 : population σ² = 0.25²
n = 30
Calculate the sample variance, s.
calculate the Χ² statistic
Χ² = (n-1)*s²/σ²
Look up the Χ² table for 29 degrees of freedom and 5 and 95% levels of confidence.
If the calculated Χ² falls between these limits, the null hypothesis is not rejected.