A certain brand of apple juice is supposed to have 64 ounces of juice. Because the penalty for under-filling bottles is so 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-filling or under-filling the bottles. She randomly samples 22 bottles of juice, measures the content, and obtains a mean of 64.022 ounces and a standard deviation of .04 ounces. She determines the data is normally distributed. Should the assembly line be shut down so that the machine can be recalibrated? Use a .01 level of significance.
a) state the null hypothesis and the alternative hypothesis
b) sketch the sampling distribution
c) determine the critical values and mark them on your sketch
d) determine the rejection region(s) and shade on your sketch
e) calculate the standardized test statistic and mark on your sketch
f) determine whether to accept or reject the null hypothesis
g) interpret your decision in the context of the original claim. (Be sure to write a complete sentence as your interpretation.)
If you are using P-tests instead of the traditional method, parts c), d), and e) become
• calculate the standardized test statistic
• determine the P-value