Twenty-five blood samples were selected by taking every seventh blood sample from racks holding 187 blood samples from the morning draw at a medical center. The white blood count (WBC) was measured using a Coulter Counter Model S. The mean WBC was 8.636 with a standard deviation of 3.9265.

(a) Construct a 95 percent confidence interval for the true mean using the FPCF.

(b) What sample size would be needed for an error of +/- 1.5 with 95 percent confidence?

a) The 95% confidence interval for the true mean is:

b) This margin of error can be achieved with a sample of size 27 individuals.

Step-by-step explanation:

a) We have to construct a 95% confidence interval for the populations mean WBC.

The sample results, from a sample size n=187, are:

As we are using the sample standard deviation to estimate the population standard deviation, we will use the t-statistic.

The degrees of freedom are:

The t-statistic for a 95% interval and 186 degrees of freedom is t=1.9728.

Now, we can calculate the margin of error of the confidence interval:

The upper and lower bound of the confidence interval are:

The 95% confidence interval for the true mean is:

b) As the confidence level is equal, the t-value is the same.

But the sample size has to be adjusted to have an margin of error of +/-1.5.

We use the formula for the margin of error:

This margin of error can be achieved with a sample of size 27 individuals.

option 1

data plot with   3 dots over 33, 1 dot over 34, 2 dots over 35, no dot over 36, 1 dot over 37, 2 dots over 38, 4 dots over 39, and 2 dot over 40.

1 and 2

step-by-step explanation: