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1. The mean of a sample of 25 measurements of the diameter of a camshafts on...

1. The mean of a sample of 25 measurements of the diameter of a camshafts on a production line was 6.7 cm. Manufacturer specifications call for a mean diameter of 7 cm. Assume the diameters are known to have a normal distribution with unknown mean, μ, and known variance, σ2 = .2 (cm)2.
a. Test H0: μ = 7 versus Ha: μ < 7 at level of significance α =.01. Find the p-value and state whether to reject the null hypothesis or not.
b. Find β(6.8) the probability of a type II error if the true mean, μ = 6.8.

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Answer #1

a) P-value=0.0004 => We Reject the null hypothesis

b) The probability of a type II error if the true mean, μ = 6.8 is β(6.8) is 0.5374

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