Question

n order to test whether camshafts are being manufactured to specification a sample of n = 35 camshafts are selected at random. The average value of the sample is calculated to be 4.44 mm and the depths of the camshafts in the sample vary by a standard deviation of s = 0.34 mm. Test the hypotheses selected previously, by filling in the blanks in the following: An estimate of the population mean is 4.44 . The standard error is 0.06 . The distribution is normal (examples: normal / t12 / chisquare4 / F5,6). The test statistic has value TS= . Testing at significance level α = 0.01, the rejection region is: less than and greater than (2 dec places). Since the test statistic (is in/is not in) the rejection region, there (is evidence/is no evidence) to reject the null hypothesis, H0. There (is sufficient/is insufficient) evidence to suggest that the average hardness depth, μ, is different to 4.5 mm. Were any assumptions required in order for this inference to be valid? a: No - the Central Limit Theorem applies, which states the sampling distribution is normal for any population distribution. b: Yes - the population distribution must be normally distributed.

Answer 1

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