Question

The following are six observations collected from treatment 1, ten observations collected from treatment, and eight observations collected from treatment 3. Test the hypothesis that the treatment means are equal at the 0.05 significance level

??⭐️

The following are six observations collected from treatment 1, ten observations collected from treatment 2, and eight observations collected from treatment 3. Test the hypothesis that the treatment means are equal at the 0.05 significance level Treatment 1 Treatment 2 Treatment 3 6 2 6 5 5 1 6 8 5 1 5 4. 4 1 7 6 4 Click here for the Excel Data File a. State the null hypothesis and the alternate hypothesis. HO p1 H1 Treatment means all the same

Answer 1

Answer Date: 11/11/2019 To test the hypothesis is that the treatment means are not all the same at 5% level of significance. The null and alternative hypothesis is, H:12 = !l2 = uz H,: Treatment means are not all the same. b) The F-critical value is,

From the F distribution at 5% level of significance table, show degree of freedom treatment is, df= k-1 = 3-1 = 2 and degree of freedom error is, df g = N-k = 6 +10+ 8) -3 = 21 as result the F-critical value is 3.47. The F-critical value is 3.47. The decision rule is, Reject the null hypothesis, if the F-test statistics is higher than the F-critical value which is 3.47.

The SS Treatment, SS Error and SS total is, 1) By using Excel software, find SS Treatment, SS Error and SS total with the help of following steps: Import the data. Choose ANOVA: Single Factor from Data Analysis in Data menu. Choose Input Range and Column in Groups by. Choose Output Range. Click Ok. SS Source of Variation Between Groups Within Groups Total 46.96 53.00 99.96 From the Excel output, the SS Treatment is 46.96, SS Error is 53.00 and SS total is 99.96

An ANOVA table is, By using Excel software, find ANOVA table with the help of following steps: 1) Import the data. Choose ANOVA: Single Factor from Data Analysis in Data menu. Choose Input Range and Column in Groups by. Choose Output Range. Click OK. df F ANOVA Source of Variation Between Groups Within Groups Total SS 46.96 53.00 99.96 9.30 MS 23.48 2.52 2 21 23 e) Decision

The F-test statistics is 9.30 is greater than F-critical value which is 3.47, the null hypothesis is rejected at 5% level of significance. There is sufficient evidence that the treatment means are not all the same. The result is statistically significant.