Suppose we have a population of adults 60 years and older. We know that the popu

Question

Suppose we have a population of adults 60 years and older. We know that the population mean total cholesterol level is 200 mg/dL, with a population standard deviation of 12 mg/dL and 22% of them have diabetes.

Answer the following questions?

a) What is the population mean total cholesterol level value?

b) What is the population SD total cholesterol level value?

c) What is the population variance total cholesterol level value?

d) What is the population proportion of diabetes value?

e) Suppose we sampled 50 people from this dataset. Based on the central limit theorem and a sample size of n=50 from this population, what do we expect the

i- Shape of the sampling distribution of sample mean of total cholesterol level?

ii- Shape of the sampling distribution of estimator of diabetes prevalence?

iii- standard error of the sample mean total cholesterol level to be?

iv- standard error of the Diabetes prevalence?

v- Mean of the sampling distribution of sample means of total cholesterol level?

vi- Mean of the sampling distribution of sample proportions of diabetes?

vii- What is the margin of error when = 0.05 based on answers.

viii- Sample mean of total cholesterol?

ix - sample proportion of diabetes?

f) If we took sample of size 250, instead of 50 comment on how the sampling distribution of the sample means of total cholesterol would differ from your answers above. Specifically mention what it would do the margin of error and how something like the probability that the sample mean is larger than 205 mg/dL would change.

Explanation / Answer

a) What is the population mean total cholesterol level value?

u = 200 mg/dL [GIVEN]

b) What is the population SD total cholesterol level value?

sigma = 12 mg/dL [ANSWER, GIVEN]

c) What is the population variance total cholesterol level value?

Hence,

sigma^2 = 144 (mg/dL)^2 [ANSWER]

d) What is the population proportion of diabetes value?

As given,

p = 0.22 [ANSWER]

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e) Suppose we sampled 50 people from this dataset. Based on the central limit theorem and a sample size of n=50 from this population, what do we expect the
i- Shape of the sampling distribution of sample mean of total cholesterol level?

Approximately bell shaped by central limit theorem.

ii- Shape of the sampling distribution of estimator of diabetes prevalence?

Approximately bell shaped by central limit theorem.

iii- standard error of the sample mean total cholesterol level to be?

sigma(X) = sigma/sqrt(n) = 12/sqrt(50) = 1.697056275 [ANSWER]

iv- standard error of the Diabetes prevalence?

s = standard error = sqrt(p(1-p)/n) =    0.058583274 [answer]

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