Answer to Question #221709 in Statistics and Probability for Paschal

Question

In the past the standard deviation of weights of certain 40.0 oz filled by a machine was 0.25 oz. A random sample of 20 packages showed a standard deviation of 0.32 oz. Test the hypothesis is the apparent increase in variability significant at the 0.05 level of significance

Answer 1

$H_0:\sigma=0.25.$

$H_a:\sigma>0.25.$

Test statistic: $\chi^2=\frac{(20-1)0.32}{0.25}=24.32.$

Degrees of freedom: $df=20-1=19.$

P-value: $p=P(\chi^2>24.32)=0.1842.$

Since the p-value is greater than 0.05, fail to reject the null hypothesis.

There is no apparent increase in variability significant at the 0.05 level of significance.