Question

For a hypothesis test of H₀:p₁ − p₂ = 0 against the alternative H_a:p₁ − p₂ ≠ 0, the test statistic is found to be 2.2. Which of the following statements can you make about this finding?

		The result is significant at both α = 0.05 and α = 0.01.
		The result is significant at α = 0.05 but not at α = 0.01.
		The result is significant at α = 0.01 but not at α = 0.05.
		The result is not significant at either α = 0.05 or α = 0.01.
		The result is inconclusive because we don't know the value of p.

Answer 1

Test statistic = 2.2

Test is two tailed test.

P value = 2 * P(z > 2.2)

= 2 * (1 - P(z < 2.2))

= 2 * (1 - 0.9861) (From statistical table of z values)

= 2 * 0.0139

P value = 0.0278

For alpha = 0.05

P value < alpha

So we reject null hypothesis H0.

The result is significant at alpha = 0.05

For alpha = 0.01

P value > alpha

So we fail to reject null hypothesis H0.

The result is insignificant at alpha = 0.01

The result is significant at α = 0.05 but not at α = 0.01.