The output of a chemical process is monitored by taking a sample of 20 vials to...

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The output of a chemical process is monitored bytaking a sample of 20 vials to determine the level of impurities.The desired mean level of impurities is 0.048 grains per vial. Ifthe mean level of impurities in the sample is too high, the processwill be stopped and purged; if the sample mean is too low, theprocess will be stopped and the values will be readjusted.Otherwise, the process will continue.
a)Â Â Sample results provide sample mean to be equal to0.057 gram with sample standard deviation equal to 0.018. At asignificance level of 0.01, should the process be stopped? If so,what type of remedial action will be required?
b)Â Â Assume that the mean level of impurities is withintolerable limits. If the maximum tolerable variability of theprocess is 0.0002, do the sample results verify the suspicion thatthe maximum tolerable variability has been exceeded? Use a 5% levelof significance.

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Solution Let X the level of impurities grains per vial Let and be respectively the mean and standard deviation of X Part a Claim The mean level of impurities in the sample is too high Hypotheses Null H0 0 0048 Vs Alternative HA 0048 claim Test statistic t nXbar 0s where n sample size Xbar sample average s sample standard deviation Summary of Excel Calculations is given below See Answer

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