Question

Calculate the margin of error of a confidence interval for the difference between two population means using the given information. Round your answer to six decimal places.

σ1=5.94σ1=5.94, n1=98n1=98, σ2=2.87σ2=2.87, n2=79n2=79, α=0.05

Answer 1

As given in the question:

Margin of error for the difference between two population means is given by:

Where is the critical value of z-test at 0.05 level of significance. Here we used z-test because population standard deviations are given, in case sample standard deviations are given we will use t-test instead of using z-test.

Critical value of z-test = 1.96 (using z-table) (for two tails)

Now by putting all the values in the formula,

M.E. = 1.3355372772

M.E. = 1.335537 (Rounded to six decimal places)