Question

I need help with - d) Assuming the residuals are normally​ distributed, test H_o : β1=0 versus H₁ : β1 ≠ 0 at the α = 0.05 level of significance - at the bottom of the page. Thank you!

For the data set shown​ below.

x   y
20   98
30   95
40   89
50   85
60   72

​(a) Use technology to find the estimates of β0 and β1.

β0 ≈ b0= 112.6

​(Round to two decimal places as​ needed.)

β1 ≈ b 1equals= −0.62

​(Round to two decimal places as​ needed.)

​(b) Use technology to compute the standard​ error, the point estimate for σ.

se = 3.1833

​(Round to four decimal places as​ needed.)

​(c) Assuming the residuals are normally​ distributed, use technology to determine sb1.

sb1 = 0.1007

​(Round to four decimal places as​ needed.)

d) Assuming the residuals are normally​ distributed, test H_o : β1=0 versus H₁ : β1 ≠ 0 at the α = 0.05 level of significance.

Use the​ P-value approach.

Answer 1

Ans:

d)

Test statistic:

t=b1/sb1

t=-0.62/0.1007

t=-6.157

df=5-2=3

p-value=tdist(6.157,3,2)=0.0086

As,p-value<0.05,we reject the null hypothesis.