The sodium content of thirty 300-gram boxes of organic corn flakes was determined. The data (in milligrams) are as follows:

131.15, 130.69, 130.91, 129.54, 129.64, 128.77, 130.72,

128.33, 128.24, 129.65, 130.14, 129.29, 128.71, 129.00, 129.39,

130.42, 129.53, 130.12, 129.78, 130.92, 131.15, 130.69, 130.91,

129.54, 129.64, 128.77, 130.72, 128.33, 128.24, and 129.65.

(a) Can you support a claim that mean sodium content of this brand of cornflakes is 130 milligrams? Use α = 0.05.

(b) Is there evidence that sodium content is normally distributed?

(c) Compute the power of the test if the true mean sodium content is 130.5 miligrams.

(d) What sample size would be required to detect a true mean sodium content of 130.1 milligrams if we wanted the power of the test to be at least 0.75?

(e) Explain how the question in part (a) could be answered by constructing a two-sided confidence interval on the mean sodium content.