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 39.017, 38.998, 39.011, 39.009, 39.014, and 39.003. We denoted the population mean thickness by mu 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 sigma - 0.008 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 H_0 at the 5% level? A. H_0 cannot be rejected. B. H_0 can be rejected.

Explanation / Answer

here sample mean of above observations Xbar =(39.017+38.998+39.011+39.009+39.014+39.003)/6 =39.00867

also std error =std deviation/(n)1/2 =0.0033

hence test stat z=(X-mean)/std error =(39.00867-39)/0.0033=2.6536

for above p value=0.0080

as p vlaue is less then 0.05 level;

Ho can be rejected. Option B

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