Question

Consider the data set below.

xx	55	22	66	33	22	77
yy	99	22	99	88	33	66

For a hypothesis test, where H0:β1=0H0:β1=0 and H1:β1≠0H1:β1≠0, and using α=0.01α=0.01, give the following:
(a)    The test statistic

t=t=
(b)    The degree of freedom

df=df=
(c)    The rejection region

|t|>|t|>
The final conclustion is

A. There is not sufficient evidence to reject the null hypothesis that β1=0β1=0.
B. We can reject the null hypothesis that β1=0β1=0 and accept that β1≠0β1≠0.

Answer 1

The statistic software output for this problem is :

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = 2.3649635 + 0.91240876 x
Sample size: 6
R (correlation coefficient) = 0.63708381
R-sq = 0.40587578
Estimate of error standard deviation: 2.6374617

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	2.3649635	2.5393803	≠ 0	4	0.93131522	0.4044
Slope	0.91240876	0.55195225	≠ 0	4	1.6530574	0.1737

(a)    The test statistic

t = 1.653
(b)    The degree of freedom

df = 4
(c)    The rejection region

|t| > 4.604

(d)

A. There is not sufficient evidence to reject the null hypothesis that β1=0