Question

You are given the value of beta, 0.32, and the value of its standard error, 0.12. The model is estimated over 40 observations.

a. Write the null (beta is not significant) and alternative hypotheses. Test the null hypothesis against a two-sided alternative. [20 marks]

b. Obtain and interpret a 99% confidence interval for beta. [20 marks

Answer 1

You are given the value of beta, 0.32, and the value of its standard error, 0.12. The model is estimated over 40 observations.

Beta: Slope of the regression. The coeffcient of 'x' in the regression equation is slope. It tells the magnitude and direction of change in 'y' due to unit change in 'x'.

a. Write the null (beta is not significant) and alternative hypotheses. Test the null hypothesis against a two-sided alternative.

Test

this is two tailed test

Test Stat =

The null beta = 0

The denominator is the SE = 0.12

Test stat = 0.32 / 0.12

Test Stat = 2.6667

n = 40

p-value = 2P(t_n-2 > |Test Stat| )

=2P(t₃₈ > 2.67)

=2 * 0.0055

p-value = 0.0111

since p-value < 0.05 (level of significance)

We reject the null hypothesis at 5%. There is sufficient evidence to conclude that the beta is not 0.

b. Obtain and interpret a 99% confidence interval for beta.

Confidence interval

(1- )% is the confidence interval for population slope

Where = 1 - 0.99 = 0.01

Critical value =                   .............found using t-dist tables

=t_38,0.005

C.V. = 2.7116

SE = 0.12

Subsituting the values

(0.32 - 0.12 * 2.7116, 0.32 + 0.12*2.7116)

Ans: (-0.0054, 0.6454)

Interpretation: We are 99% confident that true beta lies within this interval.