Question

Comparing Two Population Means with Known Standard Deviations

In this problem you do know the population standard deviation of these independent normally distributed populations

The mean for the first set ¯xx¯ ₁ = 15.49 with a standard deviation of σσ ₁ = 2.5 There sample size was 13.

The mean for the first set ¯xx¯  2  = 15.796 with a standard deviation of σσ ₂ = 1.4 There sample size was 18.

Find the test statistic z=   Round to 4 places.

Find the P-value for a left tail test.   Use the rounded version of z to 2 decimal places. Then round the P-value to 4 places.

Answer 1

The test statistic

P-value = 0.3446

The complete solution of above question are as below

The null and alternative hypothesis are

The values provided in the above question are as below

The formula of test statistic is

Under the null hypothesis

The formula of test statistic becomes

------------------(1)

By using formula of equation (1) we get

(Round answer up to 2 decimal places)

The test statistic

Now we find P-value of above test statistic using following Excel function

=NORMSDIST(z)

Here, z = -0.40

=NORMSDIST(-0.40) then press Enter we get P-value as below

P-value = 0.344578 0.3446 (Round answer up to 4 decimal places)

P-value = 0.3446

Summary :-

The test statistic

P-value = 0.3446