A manufacturer of chocolate chips would like to know whether it’s bag filling ma

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 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 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

Explanation / Answer

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

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