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The true mean breaking strength of yarn used in manufacturing drapery material is required to be above 100 psi. From past data, the standard deviation of breaking strength is known to be 2 psi. Assume that strength of yarn specimen follows normal distribution. Suppose the manufacturer decides to reject the null hypothesis whenever the sample average of 9 specimens exceeds 100.9 psi.
a) State the appropriate null and alternative hypotheses.
b) Find the probability of Type I error associated with the given rejection procedure.
c) Find the probability of Type II error if the true mean breaking strength is 101.5.
d) Suppose a sample of 9 specimens of yarn resulted in an average breaking strength of 100.8 psi. Find the p-value associated with the tests of hypothesis in (a) and draw your conclusions.
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