A manufacturer produces a special alloy steel with an average tensile strength of 25,800 psi. The standard deviation of the tensile strength is 300 psi. Strengths are approximately normally distributed. A change in the composition of the alloy is tried in an attempt to increase its strength. A sample consisting of eight specimens of the new composition is tested. Unless an increase in the strength is significant at the 1% level, the manufacturer will return to the old composition. Standard deviation is not affected.
a) If the mean strength of the sample of eight items is 26,100 psi, should the manufacturer continue with the new composition?
b) What is the minimum mean strength that will justify continuing with the new composition?
c) How large would the true mean strength of the new composition (i.e., a new population mean) have to be to make the odds 9 to 1 in favor of obtaining a sample mean at least as big as the one specified in part (b)?