Question

7. (9 points) F-test The alcohol content in a soy sauce produced on two different production lines is be- lieved to have different variances. The Minitab output from an analysis is shown below. Descriptive Statistics: content Statistics Variable lineNN content 1 3 0 2 0 Mean SE Mean Ste Minimum 01 Mediano ) Maomum 4663 0.0195 00553 03900 0.4050 043000 52000 5200 .33857 000508 001345 0.370000380000.90000 40000 41000 (a) (9 points) Utilize the classical approach to conduct an F-test to determine if the variance of the alcohol content varies by production line (two-tailed test). Use Q=0.05.

Answer 1

Answer Date: 07/10/2019 To test the hypothesis is that the variance of alcohol content varies by production line at 5% level of significance. The null and alternative hypothesis is, H,:01 = 02 H2:07 +02 The F-test statistics is, (0.0553) (0.01345) = 16.90 The F-test statistics is 16.90.

The F critical value is, From the F distribution at 5% level of significance table, show degree of freedom numerator 7 (n-1) and degree of freedom denominator 6 (7-1) and two-tailed F critical value is 5.70. The F critical value is 5.70 Decision The F-test statistics is 16.90 is higher than F critical value which is 5.70, the null hypothesis is rejected at 5% level of significance. There is sufficient evidence that the variance of alcohol content varies by production line. The result is statistically significant.