Question

Test the hypothesis that metabolic rate differs among spider species, while controlling for differences in size (abdomen length).

1) State all relevant hypotheses (nulls and alternatives).

2) State which test was used and why you used it.

3) State conclusions after completing your analyses.

Abdomen length	metabolic rate	Species
12	76	orb
18	70	orb
23	69	orb
31	63	orb
38	55	orb
42	55	orb
10	59	argiopes
15	51	argiopes
24	49	argiopes
28	47	argiopes
36	36	argiopes
44	34	argiopes
13	40	southern house
19	32	southern house
22	30	southern house
34	25	southern house
39	22	southern house
47	11	southern house

Answer 1

1) Null hypothesis ->
Alternative hypothesis -> .

2) ANOVA is used here so as to compare the mean metabolic rates among different species. ANOVA is basically used to compare means among different groups(usuallly >2) and no. of groups here is 3, so we use ANOVA.

3) R codes :

> data1=read.csv(file.choose(),header=T)
> names(data1)
[1] "Abdomen.length" "metabolic.rate" "Species"   
> attach(data1)
> model=aov(metabolic.rate~Species)
> summary(model)
Df Sum Sq Mean Sq F value Pr(>F)
Species 2 4332 2166.2 24.98 1.68e-05 ***
Residuals 15 1301 86.7   
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Since p-value is very small, we reject the null hypothesis and conclude that the means are significantly different,i.e, metabolic rate significantly differs among spider species.