Question

A farmer wanted to know if the amount of feed consumed by his chickens would be affected by the presence or absence of hatchlings. Two groups of chickens were raised from hatching either singly or in a group of five hatch-mates. At the age of six weeks, all subjects were placed in a small cage with a same-aged, group-reared chicken (in the case of group-reared subjects, the test chicken was from a different group). The following data represents the amount of grain consumed (in grams) during a 30-minute test period.

Group reared                                 Individually reared

            35                                                        9

            27                                                        16

            29                                                        13

            9                                                          13

            37                                                        26

            25                                                        11

            28                                                        5

            26       

            45

            19

Independent variable/s:

Levels of independent variable/s:

Dependent variable/s:

Test to use:

Does the presence of hatch-mates affect the amount of food consumed in the trial period?

Value of YOUR test statistic

p-value from test:

Please show steps with answers so I can understand where numbers came from.

Answer 1

(i) The independent variables are (a) Group reared chickens and (b) Individually reared chickens

(ii) As there are two types of chickens group reared and individually reared so the level of independent variables is two (2).

(iii) Dependent variable is that variable which depends on the independent variable. Here amount of grain consumed depends on the number of chickens so it is dependent variable.

(iv) As, we are testing between the means of two independent variables we are using "t" test equality of means assuming unequal variances.

(v) Null Hypothesis: Amount of food consumed are same by the presence or absence of hatchmates in trial period

Alternative Hypothesis: Amount of food consumed are not same by the presence or absence of hatchmates in trial period

Value of the test statistics obtained from the following table is t Stat is 3.406631

t-Test: Two-Sample Assuming Unequal Variances
	Variable 1	Variable 2
Mean	27.88889	13.28571
Variance	109.3611	43.57143
Observations	9	7
Hypothesized Mean Difference	0
df	14
t Stat	3.406631
P(T<=t) one-tail	0.002128
t Critical one-tail	1.76131
P(T<=t) two-tail	0.004256
t Critical two-tail	2.144787

(vi) Since this a two tailed test the p value which is being obtained is 0.004256.

Conclusion: We are conducting the test at 5% level of significance.Since calulated p value (.004256) is less than 0.05 the null hypothesis is rejected. We can conclude that the amount of hatchmates during the trial period affect the consumption of food.