Question

# Consider the data set below. xx 55 22 66 33 22 77 yy 99 22 99...

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.

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

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