Question

Question 2

The Body Mass Index (BMI) is a value calculated based on the weight and the height of an individual. In a

small European city, a survey was conducted one year ago to review the BMI of the citizens. In the sample

with 200 citizens, the mean BMI was 23.3 kg/m2 and standard deviation was 1.5 kg/m2 . It is reasonable to

assume the BMI distribution is a normal distribution.

(a) Find the point estimate of the population mean BMI one year ago.

(b) Calculate the sampling error at 90% confidence.

(c) Construct a 90% confidence interval estimate of the population mean BMI one year ago.

This city launched a healthy exercise program to reduce citizen’s BMI after last year’s survey. Suppose the

program effectively reduces the BMI of each citizen by 2.5%.

(d) Construct a 98% confidence interval estimate of the population mean BMI after the healthy exercise

program. (Hint: find the updated sample mean and sample standard deviation of the BMI of the sample

with 200 citizens selected last year)

Answer 1

Answer:

2)

a)

The point estimate of the population mean would be the sample mean. So in this case 23.3 kg/m3 is the point estimate of the population mean BMI one year ago.

b)

To calculation the sampling error at 90% confidence we use the following formula:

z* at 90% confidence is 1.645

sigma = 1.5

n = 200

We say that the sampling error is 0.17 at 90% confidence level

c)

To construct a 90% confidence interval we can use the following formula:

d)

We must first find the updated sample mean and sample standard deviation:

Then we can use the confidence interval formula to construct a 98% confidence interval:

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