Question

In testing the difference between two population means using two independent samples, the population standard deviations are assumed to be unknown, each sample size is 30, and the calculated test statistic z = 2.56. If the test is a two-tailed and the 5% level of significance has been specified, the conclusion should be:

	a.	none of these answers is correct.
	b.	choose two other independent samples.
	c.	reject the null hypothesis.
	d.	not to reject the null hypothesis.

Answer 1

z = 2.56

1) P-value approach

P-value = P( |Z| > z)......... where Z follows normal(0,1)

= P( |Z| > 2.56)

= 2 * P(Z > 2.56 )

= 2 * ( 1-P( Z < 2.56) )

= 2 * ( 1- 0.9948)

= 2* 0.0052

= 0.0105

P-value = 0.0105

We reject Ho if P-value < alpha = level of significance

Alpha = 0.05

Here P-value = 0.0105 < alpha = 0.05

We reject Ho.

2) using a critical value approach

Zc = Zalpha/2  = Z 0.05/2  = Z0.025 = ?

In Normal probability table find value 0.025 & corresponding row value + column value = Zc

Here Zc = 1.96

We reject Ho if Z > Zc

Here Z = 2.56 > Zc = 1.96

We reject Ho.

Answer:- c) reject the null hypothesis