Question: Specifications for a certain type of ribbon call for a mean breaking strength of 185 lb. In order to monitor the process, a random sample

Specifications for a certain type of ribbon call for a mean breaking strength of 185 lb.

In order to monitor the process, a random sample of 30 pieces, selected from different rolls, is taken each hour and the sample mean used to decide if the mean breaking strength has shifted. The test then is of the hypothesis Ho∶ ???? = 185 against the alternative hypothesis Ha∶ ???? < 185 with ???? = 0.05. Assuming ???? = 10 lb,

(a) Find the critical region in terms of X.

(b) Find ???? for the alternative ???? = 179.5.

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