In order to test whether camshafts are being manufactured tospecification a sample of n = 50 camshafts are selected at random.The average value of the sample is calculated to be 4.38 mm and thedepths of the camshafts in the sample vary by a standard deviationof s = 0.42 mm.
Test the hypotheses selected previously, by filling in theblanks in the following:
- An estimate of the population mean is .
- The standard error is .
- The distribution is  (examples: normal / t12 /chisquare4 / F5,6).
The test statistic has value TS=Ă‚Â Ă‚Â .
Testing at significance level α = 0.01, the rejection regionis:
less than  and greater than  (2 decplaces).
Since the test statistic  (is in/is not in) therejection region, there (is evidence/is no evidence) toreject the null hypothesis, H 0.
There  (is sufficient/is insufficient) evidenceto suggest that the average hardness depth, μ, is different to 4.5mm.
Were any assumptions required in order for thisinference to be valid?
a: No - the Central Limit Theorem applies, which states thesampling distribution is normal for any populationdistribution.
b: Yes - the population distribution must be normallydistributed.
Insert your choice (a or b): .
