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Hypothesis Testing with Types of Errors

3. At a food processing plant, a machine produces 10 lb bags of sugar. In this particular process, it is important that the sugar content does not go below 9.9 lbs. In fact, when the bags of sugar are less than 9.9 lbs, maintenance is performed on the machine. Consider a hypothesis test where:

Ho: X > 9.9 lbs. (In this case operation is continued)
Ha: X < 9.9 lbs. (In this case maintenance is performed on the machine)

Assume the population standard deviation (sigma) is 0.5 and the sample size (n) is 100. Calculate the values for alpha, a type I error and beta, a type II error. (To calculate Beta, consider a mean that is 1 standard error away from the lower end value to perform maintenance)

Solution Summary

This solution uses the null and alternative hypothesis to calculate the z test statistic and to compared with the calculated p-value to either accept or reject the null hypothesis. It also finds the probability of accepting the null hypothesis assuming that that the alternative is true.