The cherry Canning Company (CCC) of Traverse city has introduced a new manufactu

Question

The cherry Canning Company (CCC) of Traverse city has introduced a new manufacturing method to streamline the canning process of cherries. Although the time to fill a can has been reduced, the quality control manager is concerned about the uniformity of the amount of cherries in each can. The cans are labeled to contain 14.5 ounces of cherries and natural juice. To be sure that this level has not been affected by the new method, the manager randomly samples 25 cans over an eight hour shift. The mean number ounces in this are 14.66 with a standard deviation of 0.4 ounces. Has the new method changed the amount of cherries that should be in the can? a) State the null and alternative hypotheses for this experiment. b) What is the type I error for this particular application and what are its consequences? c) What is the type II error for this particular application and what are its consequences?

Explanation / Answer

given n =25

mean=14.5

x^ = 14.66

standard deviation =25

a) HO:mean mu = 14.66

   Ha: meam mu < =14.66

b) type 1 error rejecting HO even though it is true

z =( 14.66-14.5) / 0.4 sqrt25 = 0.37

from standard z table the value of 0.37 is 0.6443

which is the probbaility of type 1 error

c) type two error is when we reject alternative hypothesis when null hypothseis true

1-0.6443 =0.3557

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