Given the following values from random samples means from 4 treatments, complete

Question

Given the following values from random samples means from 4 treatments, complete the ANOVA table and tell whether to accept or reject the hypothesis that mu_1 = mu_2 = mu_3 = mu_4 at the 5% level. Given the following values from random samples means from 5 treatments, complete the ANOVA table and tell whether to accept or reject the hypothesis that mu_1 = mu_2 = mu_3 = mu_4 = mu_5 at the 5% level. Given the following values from random sample means from 3 treatments, complete the ANOVA table and tell whether to accept or reject the hypothesis that mu_1 = mu_2 = mu_3 at the 1% level.

Explanation / Answer

1) There are four treatments so degrees of freedom corresponding to treatments is k - 1 = 4 - 1 = 3

There are total observations are 12 so degrees of freedom corresponding to total is n - 1 = 12 - 1 = 11

Degrees of freedom corresponding to error = n - k = 12 - 4 = 8

MST = SST / (k - 1) = 1628.6 / 3 = 542.8667

MSE = SSE / (n - k) = 315.322 / 8 = 39.4153

F ratio = MST / MSE = 542.8667 / 39.4153 = 13.77

Degrees of freedoms are

df1 = 3

df2 = 8

Critical value = 4.066 ( Using F table)

Anova table

F test statistic > critical value we reject the null hypothesis.

Conclusion: At least one mean is different.

P-value = P(F > 13.77) = 0.0016

Source SS DOF MS Fratio Critical value Treatment 1628.6 3.000 542.867 13.77301 4.066 Error 315.322 8.000 39.41525 Total 1943.92 11.000

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