Question

Solve the following hypothesis test problems (hint: use the t-tables in the document “Formulas and Tables” as the reference guide for computing the critical value)

5.) significance level: 5% Sample size: 102 Model: y=alpha + beta*x SE(alpha): 4.23 Alpha: 14.62 Beta: 3.67 SE(beta): 1.589 a) Test for HO: beta=0 significance level: 1% Sample size: 102 Model: y=alpha + beta*x Alpha: 14.62 SE(alpha): 4.23 SE(beta): 1.589 Beta: 3.67 b) Test for HO: beta=0 → Why are the results for both models different? Why does it play a role?

Answer 1

First, let's find out the t-critical value from the t-table at 5% and 1% significance level.

df = n - p - 1 = 102 - 1 - 1 = 100

t-critical value at 5% significance level = +1.984 and -1.984
t-critical value at 1% significance level = +2.626 and -2.626

a) Ho: beta = 0

t-statistic = Coefficient/SE = 3.67/1.589 = 2.31

As t-statistic = 2.31 > 1.984, we reject the null hypothesis.

b) Ho: beta = 0

t-statistic = Coefficient/SE = 3.67/1.589 = 2.31

As 2.31 < 2.626, we fail to reject the null hypothesis.

The results in both models are different because of the significance level we are using. In the first model, we are using 5% significance level which means that there is a 5% probability of rejecting a null hypothesis when it is really true. 5% probability to make a type - 1 error. In the second model, it is 1% which is less for Type-1 error.