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The product quality manager in a bread company is concerned about whether bread weights are quite consistent with its standard weight. The parameter of interest for the manager is the population variance of the bread weight.
Let X denote the random variable indicating the bread weight. The manager selected a random sample of 101 breads and reports that the sample mean for X is 2 and the sample variable for X is 1.2.
(a) While the manager believes that the population variance for X does not exceed 1 (null hypothesis), the manager is seeking for the evidence to judge whether the population variance indeed exceeds 1. Carry out a hypothesis testing for the manager.
(b) Estimate the 95% confidence interval for the population variance of bread weights.
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