Question

A sample of n = 10 scores has a mean of 50. a second sample has n = 5 scores and m = 60. if the two samples are combined, the sample mean for the combined sample will be greater than 55.​ true

Answer 1

Solution:  We are given the sample mean of n = 10, is 50. Therefore, the sum of 10 observations is 10 x 50 = 500

The sample mean of n = 5, is 60. Therefore, the sum of 5 observations is

5 x 60 = 300

The sum of two samples is 500 + 300 = 800.

And the sum of two sample size's is 10 + 5 = 15

Now, the combined mean is:

$\frac{800}{15}=53.33$

Therefore, the given statement "the sample mean for the combined sample will be greater than 55" is false