From a long experience with a process for manufacturing analcoholic beverage it

Question

From a long experience with a process for manufacturing analcoholic beverage it is known that the yield is normallydistributed with a mean of 500 and a known population standarddeviation of 96 units. For a modified process the yield is 535units for a sample size of 50. at alpha=0.05 does the modifiedprocess increase the yield?
Question:
What test statistics should be used Z or t, and what are the valuesof our test statistics from the data and what value do we compareit to? Do we reject the Ho? Desribe the results.

Also, state the null and alternatice hypothesis.

Explanation / Answer

X~Normal (=500, =96) xbar =535, n=50 =0.05, Z(0.05) =1.645 (check normal table) The test hypothesis is Ho: 500 The test statistics is Z=(xbar - ) /(/n) =(535-500) / (96/sqrt(50)) = 2.58 Since Z=2.58 > 1.645 , we reject Ho.

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