Question

The nutrition label for Oriental Spice Sauce states that one package of sauce has 1070 milligrams of sodium. To determine if the label is accurate, the FDA randomly selects 200 packages of Oriental Spice Sauce and determines the sodium content. The sample has an average of 1012.73 milligrams of sodium per package with a sample standard deviation of 234.28 milligrams. Step 1 of 2 : 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 403.6 milligrams and 1621.86 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 = 200 - 1 = 199

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 199 degrees of freedom(y-axis) and a confidence level of
`1 - (1 - 0.99)/(2) = 0.995`. So we have T = 2.6

The margin of error is:

M = T*s = 2.6*234.28 = 609.13.

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 1012.73 - 609.13 = 403.6 milligrams

The upper end of the interval is the sample mean added to M. So it is 1012.73 + 609.13 = 1621.86 milligrams

The 99% confidence interval for the mean sodium content in Oriental Spice Sauce is between 403.6 milligrams and 1621.86 milligrams