Need help with statistics question please. 25. Filling Bottles A certain brand of apple juice is supposed to have 64 ounces of juice. Because the punishment for under filling bottles is severe, the target mean amount of juice is 64.05 ounces. However, the filling machine is not precise, and the exact amount of juice varies from bottle to bottle. The quality-control manager wishes to verify that the mean amount of juice in each bottle is 64.05 ounces so that she can be sure that the machine is not over- or under filling. She randomly samples 22 bottles of juice and measures the content and obtains the following data:
64.05 64.05 64.03 63.97 63.95 64.02 64.01 63.99 64.00 64.01 64.06 63.94 63.98 64.05 63.95 64.01 64.08 64.01 63.9 63.97 64.10 63.98

(a) Because the sample size is small, she must verify that the amount of juice is normally distributed and the sample does not contain any outliers. The normal probability plot and box plot are shown. Are the conditions for testing the hypothesis satisfied?

(b) Should the assembly line be shut down so that the machine can be re calibrated? Assume =0.06 ounces and use a 0.01 level of significance.

(c) Explain why a level of significance = 0.01 of might be more reasonable than 0.1 [Hint: Consider the consequences of incorrectly rejecting the null hypothesis.]