Question

The following information is obtained from two independent samples selected from two populations. n1=270 x¯1=5.98 σ1=1.11 n2=210 x¯2=5.40 σ2=2.47 Test at the 2% significance level if μ1 is greater than μ2 (one-tailed test). μ1 is Choose the answer from the menu in accordance to the question statement μ2 .

Answer 1

To test against

The test statistic can be written as

which under H₀ follows a standard normal distribution.

We reject H₀ at 2% significance level if P-value < 0.02

Now,

The value of the test statistic =

P-value =

Since P-value < 0.02, so we reject H₀ at 2% significance level and we can conclude that μ1 is significantly greater than μ2