The strength of a certain type of rubber is tested by subjec

The strength of a certain type of rubber is tested by subjecting pieces of the rubber to an abrasion test. For the rubber to be acceptable, the mean weight loss ? must be less than 3.5 mg. Twenty five pieces of rubber that were cured in a certain way were subject to the abrasion test. From these 25 observations, we computed a mean 3.27 mg and a standard deviation of 0.75 mg. Assume that weight loss is normally distributed. Do we have significant evidence that this type of rubber is acceptable at a level of significance of 5%?

(a) Use a 95% upper confidence bound for the mean weight loss to answer the question.

(b) Use a p-value to answer the question.

Solution

(a) Given a=1-0.95=0.05, Z(0.05) = 1.645 (from standard normal table)

So the upper bound is

xbar+ Z*s/vn= 3.27 +1.645*0.75/sqrt(25) =3.51675

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(b) The test statistic is

Z=(xbar-mu)/(s/vn)

=(3.27-3.5)/(0.75/sqrt(25))

=-1.53

It is a left-tailed test

So the p-value = P(Z<-1.53) =0.063 (from standard normal table)

Since the p-value is larger than 0.05, we do not reject the null hypothesis.

So we can not conclude that the mean weight loss ? must be less than 3.5 mg.