The sodium content of twenty 300-gram boxes of organic cornflakes 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.
a. can you support a claim that mean sodium content of this brand of cornflakes differs from 130 milligrams? use α = 0.05. find the p-value.
b. check that sodium content is normally distributed.
c. compute the power of the test if the true mean sodium content is 130.5 milligrams.
d. what sample size would be required to detect a true mean sodium content of 130.1 milligrams if you 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.