Question

Suppose that an anxiety measure has a mean of 116 and variance of 324.00. The researcher only wants to work with 47% of the lower participants. What is the largest average score the researcher should consider with a sample size of 32?

Answer 1

Solution:

Given:

Mean =

Variance =

Thus standard deviation =

Sample size = n = 32

The researcher only wants to work with 47% of the lower participants.

We have to find the largest average score the researcher should consider.

That is find sample mean such that

Since sample size = n = 32 > 30, we can use Central limit theorem which states that for large sample size n ,
sampling distribution of sample mean is approximately normal with mean of sample means:

and standard deviation of sample means is:

Thus find z value from z table such that:

P( Z < z ) = 0.4700

Look in z  table for Area = 0.4700 or its closest area and find corresponding z value.

Area 0.4681 is closest to 0.4700 and it corresponds to -0.0 and 0.08

thus

z = -0.08

Now use following formula to find x value:

Thus the largest average score the researcher should consider with a sample size of 32 is