A random sample of 28 boxes of cereal is taken from BigBoxMa

A random sample of 28 boxes of cereal is taken from Big-Box-Mart and the amount of sugar in each box is recorded. It is determined that the sample mean and sample standard deviation are 48.4 grams and 6.3 grams, respectively. Assume the sugar content is normally distributed.

a) Give a 95% confidence interval for the true mean sugar content.

b) Give a 95% prediction interval for the sugar content of a new cereal box that was not included in the study.

c) Suppose that Big-Box-Mart would like to advertise that the average sugar content is less than 50 grams per box for their cereal. Conduct a hypothesis test using significance level =0.05 to determine if there is convincing evidence to support their claim.

Solution