Question

Ten chickens, randomly selected, were treated weekly with a natural growth hormone. A certain quantity of the hormone (in grammes) was dissolved in 15 litres of drinking water. The weight of chickens were recorded after two weeks and the results are shown below.
feed cage #
A
B
C
D
E
F
G
H
I
J
K
L
M
Growth hormone (gm)
1
2
3
4
5
6
7
8
9
10
11
12
13
Weight (kg)
4.2
6.8
4.52
5.21
6.56
6.73
8.91
10.1
9.8
10.1
10.51
12.32
12.65
Answer the following questions
(i) State the strength of association between quantity of hormone and weight gain of chickens
(ii) What sort of effect does the hormone have on chicken weight?
(iii) What is the weight of the chicken a farmer would get without using any hormone?
(iv) The government recommends that the market weight of chickens should be between 6.5 and 9.0 kg. State the quantity of hormone that should be added to water.
(v) What will be the weight of chickens fed with 3.5g
(vi) How much hormone will a chicken weighing 10kg would have consumed?
(Use a 5% significance)

Answer 1

Suppose, random variables X and Y denote growth hormone (in gram) and weight (in kg) respectively.

(i)

Strength of association (Pearson's correlation coefficient) is given by

(ii)

We observe that correlation coefficient is highly positive (almost close to 1). Thus the hormone has a positive effect on chicken weight.

(iii)

We first obtain regression equation of Y on X as follows.

Regression equation of y on x is given by

Number of pairs of observation

In case of using no hormone,

Hence, 3.463077 kg weight of the chicken a farmer would get without using any hormone.

(iv)

We obtain regression equation of X on Y as follows.

Regression equation of x on y is given by

Number of pairs of observation

For ,

For ,

Hence, quantity of hormone to be added in water is 4.606911 gm to 7.859746 gm.

(v)

For ,

Hence, 5.901154 kg will be the weight of chickens that is fed with 3.5 g hormone.

(vi)

For ,

Hence, 9.16088 gm hormone a chicken weighing 10 kg should have consumed.