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# The yields from an ethanol-water distillation column have a standard deviation of 0. Process specification call for a target yield of 0. Management...

Part D. I don't know what is the beta is? Would you please show me some calculation. Please see attachment file Thank you!

1. The yields from an ethanol-water distillation column have a standard deviation of 0.01. Process specification call for a target yield of 0.93. Management wishes to detect any decrease in the true mean yield. a. A random sample of 8 recent batches produced the following yields. Conduct a hypothesis test to determine whether the true mean yield has decreased. Use an α = 0.01. 0.9 0.93 0.95 0.86 0.9 0.87 0.93 0.92 t Test for Hypothesis of the Mean Data Null Hypothesis μ = 0.93 Level of Significance 0.01 Sample Size 8 Sample Mean 0.9075 Sample Standard Deviation 0.03105295 Intermediate Calculations Standard Error of the Mean 0.010978876 Degrees of Freedom 7 t Test Statistic -2.049390153 Lower-Tail Test Lower Critical Value -2.997951566 p -Value 0.039801006 Do not reject the null hypothesis Calculations Area For one-tailed tests: TDIST value 0.039801 1-TDIST value 0.960199 Since the p-value is not less than 0.01 so we can say that the true mean yield has not decreased.
b. Based on the sample of 8 observations in part a, construct a 99% confidence interval for true mean yield of the process. Confidence Interval Estimate for the Mean Data Sample Standard Deviation 0.03105295 Sample Mean 0.9075 Sample Size 8 Confidence Level 99% Intermediate Calculations Standard Error of the Mean 0.010978876 Degrees of Freedom 7 t Value 3.499483297 Interval Half Width 0.038420392 Confidence Interval Interval Lower Limit 0.87 Interval Upper Limit 0.95 c. Discuss the relationship between your response to part a and part b Yes, since the population mean that is 0.93 lies inside the confidence interval so we are not able to reject our null hypothesis. So we can say that part a and part b are giving the same results. d. What is β, the probability of not rejecting the null hypothesis of part a, when in fact the true yield of the process is 0.925? What is (1-β); the probability of rejecting the null hypothesis of part a, when in fact the true yield of the process is 0.925?

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