Question

A survey investigated how many pounds heavier respondents were than their perceived ideal weight. Consider the following data for the two-factor experiment as shown to the right. Complete parts a through c.

Answer 1

We have to perform 2 way ANOVA , we can use excel.

Go to Data menu ---> Data Analysis ----> Anova : Two-Factor With Replication

File Home Insert Page Layout Formulas Data Review View Sign in Sha IE Data Analysis ED Connections 21 22 E Properties At Sort M Show Queries From Table Get External New Data Query, Le Recent Sources Get & Transform Tell me what you want to do... Clear Flash Fill - Consolidate Reapply 8-9 Remove Duplicates Relationships Text to What-If Forecast Advanced Columns Data Validation Manage Data Model Analysis Sheet Data Tools Forecast Group áll Ungroup Subtotal Refresh Filter All Edit Links Connections Sort & Filter Outline 5 Analysis Q10 f A B C D E F G H к L M N o P Q R S T 1 2 3 OK 4 Cancel 5 Data Analysis Analysis Tools Anova: Single Factor Anova: Two-Factor With Replication Anova: Two-Factor Without Replication Correlation Covariance Descriptive Statistics Exponential Smoothing F-Test Two-Sample for Variances Fourier Analysis Histogram 6 Help 7 8 9 10 11

For Input range select Entire data table.

Rows per sample = 2 ( because there are 2 observation per sample )

A B D E H L 11 West с Mid west 20 South x Northeast 18 2 Men 15 19 - OK 3 13 20 15 1 Anova: Two-Factor With Replication Input Input Range: SA$1:$E$ Rows per sample: 2 Alpha: 0.05 16 24 - 4 Women 19 18 19 Cancel 13 17 20 13 5 6 Help 7 8 9 Output options Output Range: New Worksheet Ply: New Workbook 10 11 12 13

Click on OK..

SS df 3.0625 1 ANOVA Source of Variation Sample Columns Interaction Within 55.6875 3 MS F P-value Fcrit 3.0625 0.316129 0.589346 5.317655 18.5625 1.916129 0.205502 4.066181 2.5625 0.264516 0.849176 4.066181 9.6875 7.6875 3 77.5 8 Total 143.9375 15

a)

A. H0 : Region and Gender do not interact to affect the mean response.

Ha : Region and Gender do interact to affect the mean response.

F = 0.265

P value = 0.849

As P value is greater than 0.05, we do not reject the null hypothesis H0.

C. Do not reject H0, There is insufficient evidence that region and gender do interact.

#b)

B. H0 : $\mu _{A1} = \mu _{A2} = \mu _{A3} = \mu _{A4}$

Ha : At least two regions have different averages in the discrepancy between existing and desired weight.

F = 1.916

P value = 0.206  

As P value is greater than 0.05, we do not reject the null hypothesis H0.

D. Do not reject H0 . There is insufficient evidence to indicate that at least two regions have different averages in the discrepancy between existing and desired weight.

#c)

C.H0 : $\mu _{B1} = \mu _{B2}$

Ha : There is a difference in averages in the discrepancy between existing and desired weight between the genders.

F = 0.316

P value = 0.589

As P value is greater than 0.05, we do not reject the null hypothesis H0.

D. Do not reject H0. There is insufficient evidence that there is a difference in averages in the discrepancy between existing and desired weight between the genders.