What is the effect size of the following and show workA mood

What is the effect size of the following and show work...A mood assessment in a sample of 15 gym members has a mean of 83 and a standard deviation of 5.6.
The mean in the general population on this measure is 79.5. Please note that the problem gives the sample standard deviation not the population standard deviation. Thanks

Solution

Here we have to calculate effect size for the following information.

Numer of gym members (n) = 15

mean (m) = 83

standard deviation (s) = 5.6

Mean of the general population (mu) = 79.5

The effect size can be calculated by using the formula

effect size = (mean of the population - mean of the sample) / standard deviation

effect size = (mu - m) / s

= (79.5 - 83) / 5.6

= -0.625

Also we can effect size by using the formula

effect size = t / sqrt(n)

t is the t-value with degrees of freedom (n-1) that is 14 and at 98.5 is 2.415.

effect size = 2.415 / sqrt(15) = 0.624

We see that the two values are same from the two different formulaes i.e. 0.625.

And negative effect size is the represents that the mean of the sample is larger than the mean of the population. With taking absolute value of -0.625 is 0.625.