Question

3. A study on estimating the metabolizable energy (ME) content of commercial cat fooks was conducted in 1986. Three factors were thought to influence ME content (y) of dry cat food are crude protien (x1), acid ether abstract (x2) and nitrogen-free abstract (x3). The data for 28 cats was fit to multiple regression model: y = β0 + β1x1 + β2x2 + β3x3 + with the following results: yˆ = 2.44 + 0.45x1 + 3.43x2 + 0.10x3

s βˆ1 = 0.38 s βˆ2 = 0.73 s βˆ3 = 0.36

(a) Is there sufficient evidence to suggest x1 is related to ME content? Set up the hypothesis test and test at α = 0.05

(b) Find a 95% Confidence interval for β3.

Answer 1

(a)

Null hypothesis : H_o : x1 is not related to ME content ;₁ =0

Alternate hypothesis : H_a : x1 is related to ME content ₁0(Two tailed test)

Test statistic

Degrees of freedom = n- 4 = 28-4=24

= 0.05

As p-value 0.248 is greater than :0.05 Fail to reject null hypothesis,

There is no sufficient evidence to suggest that x1 is related to ME content

(b)

95% confidence interval for

Formula for confidence interval

for 95% confidence level = (100-95)/100 = 0.05

/2 = 0.025

t_0.025 24 degrees of freedom = 2.0639

95% confidence interval for

95% confidence interval for = (-0.643004, 0.843004)