Question

Ground beef is packaged in small trays, intended to hold 1 pound of meat. A random sample of 45 packages in the small tray produced weight measurements with an average of 1.04 pounds and a standard deviation of 0.19 pound.a. If you were the quality control manager and wanted to make sure that the average amount of ground beef was indeed 1 pound, what hypotheses would you test?b. Find the p-value for the test and use it to perform the test in part a.c. How would you, as the quality control manager, report the results of your study to a consumer interest group?

Answer 1

There is sufficient statistical evidence to suggest that the average weight of the ground beef packaged in small trays is 1 pound

Explanation:

Here we have to perform a t-test

Mean = Sample mean = 1.04 lb

μ = Population mean = 1 lb

s = Standard deviation of 0.19

n = Sample size = 45

Null hypothesis H₀ = 1

Alternative hypothesis Hₐ > 1

Therefore from

`t=\frac{\bar{x}-\mu }{(\sigma )/(√(n))}` we have

t = 1.412

Critical t at 5% confidence level = 1.68

at 5 % confidence level we obtain the probability P is;

P = 0.0825 > 0.05 Therefore we accept our null hypothesis that the average weight of ground beef per pack is 1 pound.