Question

Question # 2. In this study, two independent, random samples with interval/ratio data were collected. In Group 1, a random sample of 133 primary hypertension (PH) patients were taken and each person's total cholesterol (measured in mg/dl) was recorded. In Group 2, a random sample of 41 normotensive (NT) was taken and their total cholesterol was recorded. (12 points).

Column	n	Sample Mean (x bar)	Population SD
PH	133	214.71	29.66
NT	41	193.20	33.04

(i) What is the point estimate of the primary hypertension (PH) patients’ total cholesterol mean?

(ii) Find the standard of error of the sample mean of the primary hypertension Patients’ total cholesterol.

(iii) Can you apply the central limit theorem to estimate the population

    mean of the primary hypertension Patients’ total cholesterol? Why?

(iv) Find a 90% confidence interval of the population mean of the primary hypertension Patients’ total cholesterol. Also, interpret its meaning.

Answer 1

ANSWER:

Given that,

i)

Point estimste = = 214.71 - 193.20 = 21.51

ii)

SE = sqrt()

         = sqrt((29.66)^2/133 + (33.04)^2/41)

         = 5.765

iii)

As the sample sizes are large in both the samples (n1 and n2 > 30), So we can use Central Limit Theorem.

iv)

Aat 90% confidence interval the critical value is z_0.05 = 1.645

The 90% confidence interval is

+/- z_0.05 * SE

= 21.51 +/- 1.645 * 5.765

= 21.51 +/- 9.483

= 12.027, 30.993

We are 90% confident that the difference in true population means lies in the bove interval.