Question

number of crimes (y) is affected by

unemployment (x1), number of police offcers (x2) and population (x3). 64 urban areas and found the following results.

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Test at 5% significance levels if the coefficient of unemployment

	Do not reject H0; p-value > alpha
	Reject H0; test statistics > t-table value or critical value
	Reject H0; p-value > alpha
	Do not Reject H0; p-value < alpha

Answer 1

Solution:

Here, we have to check the significance of the coefficient of unemployment by using t test for regression coefficient. The null and alternative hypotheses are given as below:

Null hypothesis: H₀: The coefficient of unemployment is not statistically significant.

Alternative hypothesis: H_a: The coefficient of unemployment is statistically significant.

We are given

Level of significance = α = 5% = 0.05

The test statistic is given as below:

t = β̂/SE

We have β̂ = 59.651, SE = 310.845, n = 64, df = n – 1 = 64 – 1 = 63

t = 59.651/310.845

t = 0.192

P-value = 0.848

(By using t-table)

[We already had given these values in the regression output.]

P-value > α = 0.05

So, we do not reject H₀

Answer: Do not reject H0; p-value > alpha

There is insufficient evidence to conclude that the coefficient of unemployment is statistically significant.