Question: In the past the standard deviation of weights of certain 32.0-oz packages filled by a machine was 0.25 oz. A random sample of 16 packages showed a standard deviation of 0.30 oz. Is the apparent increase in variability significant at the 0.10 level of significance? Assume package weight is normally distributed.

(a) State the appropriate null and alternative hypotheses.

Ho: σ 0.25 (=,<,>,not equal to)

Ha: σ 0.25 (=,<,>,not equal to)

(ii) Find χ2star. (Give your answer correct to two decimal places.)

(iii) Find the p-value. (Give your answer bounds exactly.)

< p <

(b) State the appropriate conclusion.

Reject the null hypothesis, there is not significant evidence of an increase in variability.

Reject the null hypothesis, there is significant evidence of an increase in variability.

Fail to reject the null hypothesis, there is not significant evidence of an increase in variability.

Fail to reject the null hypothesis, there is significant evidence of an increase in variability.