A textile fiber manufacturer is investigating a new drapery

A textile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. The company wishes to test the hypothesis H0: mu = 12 against H1: mu

Solution

Critical region is x bar <11.5

i.e. z score <11.5-12/0.5 = -1

Hence z value <0.1687

Significance level left is 16.87%

b) If true elongation is 11.25, then beta error will be -0.5(16.87) =8.43%

Ho: mu =25

Ha: mu<25

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Does not reject null hyp, means yes mu >=25 newtons.

Type I error = 101.5-98.5 =3%

If actual mean = 103, beta error (103-100)3% =9%