Question

A manufacturer of chocolate chips would like to know whether it’s bag filling machine works correctly at the 401 gram setting. It is believed that the machine is underfilling the bags. A 10 bag sample had a mean of 393 grams with a standard deviation of 10. Assume the population is normally distributed. Is there suffiecent evidence at the 0.02 level that the bags are under filled? Answer:

A) there is not sufficient evidence to support the claim that the bags are under filled. OR

B) there is sufficient evidence to support the claim the bags are underfilled

Answer 1

Z score = (X-Mean)/ Standard Deviation

(401 - 393)/10 = 0.8

Now, from normal distribution table, P for Z= 0.8 in one tailed analysis is = 78%

therefore, Probability that the filling is less than 401 is 78%

Since we need the evidence at 0.02 level i.e., probability should be atleast 98% that the filling is less than 401, we cannot accept the hypothesis that bags are uderfilled

Hence, A - there is not sufficient evidence to claim that the bags are under filled