Question

Consider the data in the table collected from three independent populations.

Sample_1 - 10,3,8 Sample_2 - 5,1,6 Sample_3- 4,6,3,7

a) Calculate the total sum of squares​ (SST) and partition the SST into its two​ components, the sum of squares between​ (SSB) and the sum of squares within​ (SSW).

​b) Use these values to construct a​ one-way ANOVA table.

​c) Using alphaequals0.05​, what conclusions can be made concerning the population​ means?

alphaequals0.05. ​

a) Determine the values. SSTequals ___ ​(Type an integer or a​ decimal.) SSBequals ___ ​(Type an integer or a​ decimal.) SSWequals ___​(Type an integer or a​ decimal.)

​b) Complete the​ one-way ANOVA table below.

Source Sum of Squares Degrees of Freedom Mean Sum of Squares F Between nothing nothing nothing nothing Within nothing nothing nothing Total nothing nothing ​(Type integers or decimals. Round to three decimal places as​ needed.)

​c) Let mu 1​, mu 2​, and mu 3 be the population means of samples​ 1, 2, and​ 3, respectively. What are the correct hypotheses for a​ one-way ANOVA​ test? A. Upper H 0​: mu 1equalsmu 2equalsmu 3 Upper H 1​: Not all the means are equal.

B. Upper H 0​: mu 1equalsmu 2equalsmu 3 Upper H 1​: mu 1not equalsmu 2not equalsmu 3

C. Upper H 0​: mu 1not equalsmu 2not equalsmu 3 Upper H 1​: Not all the means are equal. D. Upper H 0​: mu 1not equalsmu 2not equalsmu 3 Upper H 1​: mu 1equalsmu 2equalsmu 3 What is the critical​ F-score, Upper F Subscript alpha​? Upper F Subscript alphaequals ___ ​(Round to three decimal places as​ needed.) What is the correct conclusion about the population​ means? Since the​ F-statistic ______, _____ Upper H 0. The data _____ evidence to conclude that the population means are not all the same.

Answer 1

a) The values. SST= 64.1 SSB= 14.1 and SSW= 50

F cal= 0.987

A. Upper H0​:

Upper H1​: Not all the means are equal.

F crit=4.737

Since the​ F-statistic is smaller than F critical. DO NOT H0. The data does not have sufficient evidence to conclude that the population means are not all the same.