Question

In order to compare the means of two populations, independent random samples of 400 observations are selected from each population with the following results:

Sample 1	Sample 2
Sample Mean = 5275	Sample Mean = 5240
s1 = 150	s2 = 200

To test the null hypothesis H₀: µ₁ - µ₂ = 0 versus the alternative hypothesis H_a: µ₁ - µ₂ ╪ 0 versus the alternative hypothesis at the 0.05 level of significance, the most accurate statement is:

Answer 1

Here we have : n1 =400, n2 = 400, = 5275, s₁ = 150, = 5240, s₂ = 200

The hypothesis are :

H0: µ1 - µ2 = 0 v/s  Ha: µ1 - µ2 ╪ 0

Here we have sample standard deviations but sample sizes are large. Hence we use z test statistic. We use sample standard deviation as a estimate of population standard deviation.

The test statistic is,

= 2.8

= 0.05

The critical values are,

Here test is two tailed.

Left tailed value :

Right tailed value :

Here calculated value of z > critical value of z.

Hence we reject null hypothesis.

Conclusion : There is sufficient evidence to conclude that the two population means are different.