Question

You are a clinical psychologist and are interested in studying depression. There are no normative databases nor census data that can address what value is the population mean of depression. You decide to conduct a study to assess what the population mean of depression may be by getting the mean depression score of 31 people. Your sample has a mean of 255 and a standard deviation of 12. Calculate the 99% confidence interval for the population mean of depression.

a. Calculate the 99% confidence interval for the population mean of depression. (Write out your equation and calculate the final answer.) (4 points)

b. Interpret your confidence interval. (1 point)

Answer 1

Solution :

a) degrees of freedom = n - 1 = 31 - 1 = 30

t/2,df = t0.005,30 = 2.750

Margin of error = E = t/2,df * (s /n)

= 2.750 * (12 / 31)

Margin of error = E = 5.93

The 99% confidence interval estimate of the population mean is,

  ± E

= 255  ± 5.93

= ( 249.07, 260.93 )

b) We are 99% confident that the true mean of depression between 249.07 and 260.93.