Question

he nutrition label for Oriental Spice Sauce states that one package of sauce has 1100 milligrams of sodium. To determine if the label is accurate, the FDA randomly selects 40 packages of Oriental Spice Sauce and determines the sodium content. The sample has an average of 1088.64 milligrams of sodium per package with a sample standard deviation of 234.12 milligrams. Calculate a 99% confidence interval for the mean sodium content in Oriental Spice Sauce.

Answer 1

The 99% confidence interval for the mean sodium content in Oriental Spice Sauce is between 454.67 milligrams and 1722.61 milligrams

Explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 40 - 1 = 39

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 39 degrees of freedom(y-axis) and a confidence level of
`1 - (1 - 0.99)/(2) = 0.995`. So we have T = 2.7079

The margin of error is:

M = T*s = 2.7079*234.12 = 633.97

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 1088.64 - 633.97 = 454.67 milligrams

The upper end of the interval is the sample mean added to M. So it is 1088.64 + 633.97 = 1722.61 milligrams

The 99% confidence interval for the mean sodium content in Oriental Spice Sauce is between 454.67 milligrams and 1722.61 milligrams