Question

A group of researchers is studying the relationship between cortisol (stress hormone) levels and memory, and they want to see if a sample of 25 adults that has been recruited is a good representation of the population it came from before they conduct additional research. The population has been found to have an average cortisol level of 12 mcg/dL, with a standard deviation of 2 mcg/dL. The sample was found to have an average cortisol level of 15 mcg/DL, with a standard deviation of 3 mcg/dL.

For this assignment, construct a confidence interval to determine if this sample mean is significantly different from the population mean. Explain how you know, based on the confidence interval, and specific the confidence level you used. Be sure to show your work and calculations.

If you give a well-written answer I always give thumbs up!!!

Answer 1

Let us construct 99% confidence interval.

Calculation

M = 15
t critical= 2.8
sM = √(3^2/25) = 0.6

μ = M ± t(sM)
μ = 15 ± 2.8*0.6
μ = 15 ± 1.68

M = 15, 99% CI [13.32, 16.68].

You can be 99% confident that the population mean (μ) falls between 13.32 and 16.68.

95% confidence interval

Calculation

M = 15
t critical= 2.06
s_M = √(3²/25) = 0.6

μ = M ± t(s_M)
μ = 15 ± 2.06*0.6
μ = 15 ± 1.24

M = 15, 95% CI [13.76, 16.24].

You can be 95% confident that the population mean (μ) falls between 13.76 and 16.24.

Calculation

M = 15
t critical = 1.32
s_M = √(3²/25) = 0.6

μ = M ± t(s_M)
μ = 15 ± 1.32*0.6
μ = 15 ± 0.79

M = 15, 80% CI [14.21, 15.79].

You can be 80% confident that the population mean (μ) falls between 14.21 and 15.79.

If we compare above two we find that 80% confidence interval much closer to the population mean than the 95% and 99% confidence interval.