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# Two-way ANOVA table: f ratio, degrees freedom, null, result

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The table depicts a two-way ANOVA in which gender has two groups (male and female), marital status has three groups (married, single never married, divorced), and the means refer to happiness scores (n = 100):

What is/are the independent variable(s)? What is/are the dependent variable(s)?
What would be an appropriate null hypothesis? Alternate hypothesis?
What are the degrees of freedom for 1) gender, 2) marital status, 3) interaction between gender and marital status, and 4) error or within variance?
Calculate the mean square for 1) gender, 2) marital status, 3) interaction between gender and marital status, and 4) error or within variance.
Calculate the F ratio for 1) gender, 2) marital status, and 3) interaction between gender and marital status.
Identify the criterion Fs at alpha = .05 for 1) gender, 2) marital status, and 3) interaction between gender and marital status.
If alpha is set at .05, what conclusions can you make?
Source Sum of Squares (degrees of freedom [df]) Mean Square Fobt. Fcrit.
Gender 68.15 ? ? ? ?
Marital Status 127.37 ? ? ? ?
Gender * Marital Status (A x B) 41.90 ? ? ? ?
Error (Within) 864.82 ? ? NA NA
Total 1102.24 99 NA NA NA

https://brainmass.com/statistics/analysis-of-variance/479710

#### Solution Summary

Your tutorial is attached. I completed the table in Excel so you can click in the cells and see the computations. Instructional notes are in the table for you. References are given for online calculators of F critical.

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## ANOVA - Bottle Design

1. ANOVA EXERCISES

EXERCISE 10.18-Bottle Design (One Way ANOVA). Use Table 10.10. Complete the exercise from the data given and answer all of the questions in a written summary. (Cut and paste any EXCEL data that you wish to discuss).

A consumer preference study involving three different bottle designs (A,B, and C) for the jumbo size of a new liquid laundry detergent was carried out using a randomized block experimental design, with supermarkets as blocks. Specifically, four supermarkets were supplied with all three bottle designs, which were priced the same. Table 10.10 gives the number of bottles of each design sold in a 24-hour period at each supermarket. If we use these data, SST, SSB, and SSE can be calculated to be 586.1667, 421.6667, and 1.8333, respectively.