Suppose you have a sample of six spacer collars, whose thicknesses (in mm) are 3

Question

Suppose you have a sample of six spacer collars, whose thicknesses (in mm) are 39.015, 38.995,39.012, 39.007, 39.014, and 39.005. We denoted the population mean thickness by p and tested the hypotheses H_0: mu = 39.00 versus H_1 mu notequalto 39.00 Now assume that these six spacer collars were manufactured just after the machine that produces them had been moved to a new location. Assume that on the basis of a very large number of collars manufactured before the move, the population of collar thicknesses is known to be very close to normal, with standard deviation o - 0.010 mm, and that it is reasonable to assume that the move has not changed this. On the basis of the given data, can we reject Hq at the 5% level? H_o can be rejected. H_0 cannot be rejected.

Explanation / Answer

From information given, xbar=39.007,

Z(Obtained)=(xbar-mu)/(sigma/sqrt n)=(39.007-39)/(0.010/sqrt 6)=1.71

The Z critical at alpha=0.05 is +-1.96.

The test statistic do not fall in critical region, therefore, fail to reject H0. (option 2)

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