Question

In: Statistics and Probability

In order to compare the means of two populations, independent random samples of 400 observations are...

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 Ha: µ1 - µ2 ╪ 0 versus the alternative hypothesis at the 0.05 level of significance, the most accurate statement is:

Solutions

Expert Solution

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.


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