Question

Researchers studying factors that affect emotional state sometimes look at the saliva concentration of cortisol, a hormone that the body releases in response to stress. Saliva concentrations of cortisol in one adult human population have mean 0.75 ng/ml and a standard deviation of 0.67 ng/mL. Suppose that a random sample of 20 individuals is selected from this population, and the mean cortisol concentration is calculated.

1. (a) Calculate the mean and standard deviation for the sampling distribution of x ̄.

2. (b) For samples of this size, what must be true of the population in order for us to conclude the sampling distribution of x ̄ is normal?

3. (c) Now suppose the random sample of 20 subjects is found to have an average cortisol concentration of 0.94 ng/mL. Calculate P (x ̄ ≥ 0.94).

4. (d) Would it be considered unusual to see a sample of 20 patients with such an average concentration?

5. (e) Would it be more or less likely to see a sample of 65 people with a mean cortisol concentration greater than or equal to 0.94 ng/mL? Explain briefly, referring to the qualitative characteristics of how the shape of the sampling distribution changes with sample size.

I needed help figuring out how to do C, D, and E

Answer 1

(a)

(b)

Population of  cortisol concentration should be normally distributed.

(C)

(d)

No because above probability is not less than 0.05.

(e)

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