Question

Do Different age groups have different mean body temperatures? To answer this a researcher takes a sample of five people from three different age groups and measures their body temperature.This is a completely randomized design, run an ANOVA test to answer the researchers Question. Use α = 0.05.

Age Group 1: 18-20	Age Group 2: 21-29	Age Group 3: 30 and older
98.5	99.2	97.0
97.8	98.5	97.3
97.1	97.9	98.2
98.0	98.8	97.1
98.2	99.1	97.9

A. What is the factor in this experiment?

B. What are the treatments?

C. What is the response variable?

D Fill in the ANOVA table below.

  

Source of Variation	SS	DF	MS	F	P-Value
Treatment
Error
Total

E. Is there enough evidence to say that different age groups have different mean body temperatures? yes/no

Answer 1

step 1
null hypothesis ho :µ1 =µ2 =µ3
alternative hypothesis :µ1 ≠µ2 ≠µ3                               
step 2                                              
degrees of freedom between = k - 1 = 3 - 1 = 2                                          
degrees of freedom within = n - k = 15 - 3 = 12                                          
degrees of freedom total f( k-1,n - k,) at 0.05 is = f crit = 3.885                                          
step 3                                              
grand mean = g / n = 97.92+98.7+97.5 / 3 = 98.04                                          
sst = ∑ ( xi - grandmean)^2 = (98.5-98.04)^2 + (97.8-98.04)^2 + (97.1-98.04)^2 + ……..& so on = 7.016                                          
ss within = ∑ (xi - mean of xi ) ^2 =,(98.5-97.92)^2 + (97.8-97.92)^2 + (97.1-97.92)^2 + ……..& so on = 3.308                                          
ss between = sst - ss within = 7.016 - 3.308 = 3.708                                          
step 4                                              
mean square between = ss between / df between = 3.708/2 = 1.854                                          
mean square within = ss within / df within = 3.308/12 = 0.276                                          
step 5                                              
f cal = ms between / ms within = 1.854/0.276 = 6.726                                          
we got |f cal| = 6.726 & |f crit| =3.885                                          
make decision                                              
hence value of |f cal| > |f crit|and here we reject ho                                          
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A. it is one factor anova
B. the different age group range
C. their body temperature level for every group
D filled and added
E. reject ho, enough evidence to say that different age groups have different mean body temperatures