Question

2. Suppose that the blood cholesterol levels of all men aged 20 to 34 follows Normal distribution with mean 188 mg/dl. You wanted to check if the given value for the population mean is reasonable and you constructed a 90% confidence interval based on a sample of men aged 20 to 34 to estimate the population mean, interval is: (166 mg/dl, 202 mg/dl). Find the mean blood cholesterol level for the sample.

Answer 1

The mean blood cholesterol level for the sample is 184mg/dl

Explanation:

Hello!

When you construct any confidence interval for the mean, the general structure is "estimator±margin of error"

For example under a Z-distribution the formula is

X[bar]±
`Z_(1-\alpha/2)`*(σ/√n)

So you subtract or add "
`Z_(1-\alpha/2)`*(σ/√n)" to the sample mean. In other words, this type of confidence interval is centered on the sample mean.

If the interval is already calculated, you just have to add both limits and divide by two to get the sample mean.

[166mg/dl;202mg/dl]

sample mean: x[bar]= (166+202) = 184mg/dl

2

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