Question

Test of significance

B1=2.230

SE=0.051

Df= 148

Is B1 more than 2?

draw a graph to show p value. add the confidence interval as well. t*= 1.96

Answer 1

Solution:

Here, we have to use t test for significance of regression coefficient.

The null and alternative hypotheses are given as below:

Null hypothesis: H₀: ?₁ = 2

Alternative hypothesis: H_a: ?₁ > 2

This is a one/upper/right tailed test.

We are given

B₁ = 2.230

SE = 0.051

DF = 148

Critical t value = 1.96

Significance level = ? = 0.05

(Significance level related to given critical t value)

Test statistic = t = B₁/SE

Test statistic = t = 2.230/0.051

Test statistic = t = 43.72549

P-value = 0.00

? = 0.05

P-value < ? = 0.05

So, we reject the null hypothesis H₀

There is sufficient evidence to conclude that B1 is more than 2.

Confidence interval = B1 ± t*SE

Confidence interval = 2.230 ± 1.96*0.051

Confidence interval = 2.230 ± 0.09996

Lower limit = 2.230 - 0.09996 =2.13004

Upper limit = 2.230 + 0.09996 = 2.32996

Confidence interval = (2.13004, 2.32996)

WE are 95% confident that the population regression slope ?1 will be lies between 2.13004 and 2.32996.