Question

The Food and Drug Administration will allow a food product to be labeled “sodium free” only if there is strong evidence that it contains, on average, less than 5 milligrams of sodium per serving. A soft drink producer, wishing to use a “salt free” label, has its product tested. A laboratory takes 25 independent sample servings of the soft drink and measures them for sodium content using a technique that is practically free of bias. These measurements average 4.9 milligrams of sodium with a standard deviation of 1 milligram. Is this strong evidence that the new soft drink deserves the “salt free” label? Translate this problem into a statistical hypothesis-testing problem and carry out the test. Be sure to give the null and alternative hypotheses, the value of the test statistics, the p-value, and your conclusions.

Answer 1

Solution:

Given: The Food and Drug Administration will allow a food product to be labeled “sodium free” only if there is strong evidence that it contains, on average, less than 5 milligrams of sodium per serving.

A soft drink producer, wishing to use a “salt free” label, has its product tested.

Sample size = n = 25

Sample Mean =

Sample standard deviation = s = 1

We have to test if there is strong evidence that the new soft drink deserves the “salt free” label.

Step 1) State null and alternative hypothesis .

vs

Step 2) Find test statistic:

Step 3) P-value:

df = n -1 = 25 - 1 = 24

Look in t table for df = 24 row and find interval in which absolute t =0.500 fall and then find corresponding one tail area.

From t table we can see t = 0.500 fall between 0.000 and 0.685

corresponding one tail area is between 0.500 and 0.250

Thus range of P-value is:

0.250 < p-value < 0.500

Step 4) Decision and Conclusion:

Since 0.250 < p-value < 0.500 , that means P-value < 0.05 significance level, we fail to reject null hypothesis H0.

Thus there is no strong evidence that the new soft drink deserves the “salt free” label.