The following data were obtained from a study investigating the differences in n

Question

The following data were obtained from a study investigating the differences in number of pets per family in urban, suburban, and rural environments. Use an ANOVA with an alpha of 0.05 to determine whether there is a significant difference in the number of pets per family in the different environments. Make sure to run an entire hypothesis test, including a post hoc test if appropriate and writing the results in APA style. Environment Rural Suburban Urban 10 IXtot 48 Xot-258 N-18 0 0 0 n-6 2Xeal 30 Mean 5 2Xcol-12 Mean-2 Mean 1

Explanation / Answer

Here for doing the ANOVA the the Null hyp Ho : All means acorss type of household are equal

Ha : Not all means are equal

Now we need to calculate beween treament estimate

Now the individual sample means are 5, 2 and 1 for rural, urban and suburban

For calcluating SSTR = Sum(nj*(Xjbar - Xbarbar)^2 = 6*(5-2.66)^2 + 6* (2-2.66)^2 + 6*(1-2.66)^2 = 52

Now MSTR = STTR/k-1 = SSTR/2 = 26

For within treatments estimate we do the following computations

Now MSE = SSE/nT-k = SSE/18-3 = SE/15

where SSE = Sum(nj-1)*sj^2 , The sample variances are 11.2, 2.8 and 1.6 resp

so SSE= (6-1)* 11.2 + (6-1)*2.8 + (6-1)*1.6 = 78

so MSE = 78/15 = 5.2

Now the F statistic = MSTR/MSE = 5 where numeratord degrees of freedom = 3-1 =2 and denominator degrees of freedom = 18-3 =15

The p value computed by looking up the F table for F=5 yields , p = 0.02164 . Now p <alpha at the 0.05 level of significance, hence we will reject the null hypothesis ans hence it is proved that there is a significant difference in the number of pets owned in the different types of household

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