To examine the calming effect of pets during stressful situations, you recruited

Question

To examine the calming effect of pets during stressful situations, you recruited 52 children who owned pets and had them perform a stressful task. You randomly assigned the children into three treatment groups and had them perform the task either alone (control group), with a parent, or with their pet present. Their heart rate (in beats per minute) during the task was recorded and you calculated SSreatment 1987.3 and 2. sstotal = 6219.1. Do pulse rates differ across the three treatments? Carry out the appropriate test to answer this question and include all steps for full credit. (4pt) a. b. Calculate the appropriate fit statistic for your analysis and interpret it in the context of the problem. (2pt)

Explanation / Answer

a) here null hypothesis: Ho:all three treatment have equal mean pulse rate.

Alternate hypothesis: Ha:at least one group have different mean pulse rate.

degree of freedom between treatments =k-1 =3-1

degree of freedom with in treatment group =N-k =52-3 =49

total degree of freedom =N-1= 52-1 =51

MSTr =SStr/dftr =1987.3/2=993.65

SSE =SST-SSTr =6219.1-1987.3 =4231.8

hence MSE =SSE/dfwithin =4231.8/49 =86.36

threfore test statistic F =MSTr/MSE =11.51

b) for above test statistic and (2,49) degree of freedom ; p value =0.0001 ; whcih gives us probability of getting result as extreme or more if  all three treatment have equal mean pulse rate.

as probability of that happening is very less we reeject null hypothesis and conclude that :at least one group have different mean pulse rate.

source SS df MS F treatments 1987.3 2 993.65 11.51 within (error) 4231.8 49 86.36 total 6219.1 51

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