The yield of a chemical process follows a normal distribution. We have a sample
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Question
The yield of a chemical process follows a normal distribution. We have a sample with n = 51 and s = 0.37. a) Test the hypothesis H0 : ? = 0.25 versus H1 : ? 6= 0.25 using ? = 0.05. Make your conclusion, by finding the P-value. b) Explain how you could answer the question in part (a) by constructing a 95% two-sided confidence interval for ?.
The yield of a chemical process follows a normal distribution. We have a sample with n 51 and s-0.37 a) Test the hypothesis Ho : = 0.25 versus Hi : 0.25 using a = 0.05. Make your conclusion, by finding the P-value.Explanation / Answer
Test and CI for One Standard Deviation
Null hypothesis Sigma = 0.25
Alternative hypothesis Sigma not = 0.25
The standard method is only for the normal distribution.
The adjusted method cannot be calculated with summarized data.
Statistics
N StDev Variance
51 0.370 0.137
Ho: o=0.25
Ha: o not equal to 0.25
The test statistic is
Chisquare =(51-1)*s^2/o^2
=50*(0.37)^2/(0.25)^2
= 109.52
Given a=0.05, the critical value of chisquare with , df=n-1=50 is 67.50 (from chisquare table)
Since 109.52 is greater than 67.50, we reject Ho.
95% Confidence Intervals
Method CI for StDev Variance
Standard (0.310, 0.460) (0.096, 0.212)
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