Question

The following are data on the weights of food (in kg) consumed per day by adult deer at different times of the year month <- factor(c(rep(2,5),rep(5,6),rep(8,6),rep(11,5))) food <-c(4.7,4.9,5.0,4.8,4.7,4.6,4.4,4.3,4.4,4.1, 4.2,4.8,4.7,4.6,4.4,4.7,4.8,4.9,5.2,5.4,5.1,5.6)

(a) Test the hypothesis that food consumption is the same for all months.

(b) Report the critical results.

(c) Is food consumption the same for all months tested?

(d) What null distribution did you use?

(e) What type of variable is weight?

(f) How many factors are there?

Answer 1

Let us suppose the hypothesis

Null hypothesis:

Alternate Hypothesis:

Ha: at least one mean significantly differs from the other

Using the excel with below mentioned steps:

Data>Data Analysis>ANOVA:Single Factor >select input range>Ok

ANOVA single factor summary is given as below:

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Feb	5	24.1	4.82	0.017
May	6	26	4.333333	0.030667
Aug	6	28	4.666667	0.022667
Nov	5	26.2	5.24	0.073
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	2.306515	3	0.768838	22.08366	2.94E-06	3.159908
Within Groups	0.626667	18	0.034815
Total	2.933182	21

Here value of test statstic is 22.08

The p-value is < .00001.

The result is significant at p < .05.

P value of F test is near by zero

Assume that the significant level a=0.05

Since the p-value is less than 0.05, we would reject null hypothesis

• Based on the sample data, we can conclude that the amount of food consumed by adult deer in at least 1 (some professors say at least 2) of the 4 months significantly differs from the other months.

e)

Weight is continuous variable because it is variable

f)

One factor is present in the data