Question

A simple random sample of size n is drawn from a population that is normally distributed. The sample mean x bar is found to be

109,

and the sample standard​ deviation, s, is found to be 10.

a. Construct 95% confidence interval about miu, if the sample size n is 28. Find lower and upper bound.

​b. Construct 95% confidence interval about miu, if the sample size n is 17. Find lower and upper bound.

c.Construct 80% confidence interval about miu, if the sample size n is 28. Find lower and upper bound.

d. Could we have computed the confidence intervals in part a to c if the population had not been normally distributed?

Answer 1

Solution:

here, n=sample size.

Part(a):

Here, sample mean = .

and sample standard deviation = s = 10.

We are given, n = 28.

The 95% confidence interval wil be:(109 - 3.7, 109 + 3.7) = (105.3, 112.7) .

Upper Bound = 105.3

Lower Bound = 112.7

Part(b):

Now, are given that n = 17.

The 95% confidence interval wil be:(109 - 4.75, 109 + 4.75) = (104.25, 113.75) .

Upper Bound = 104.25

Lower Bound = 113.75

Part(c):

Now, are given that n = 28.

The 80% confidence interval wil be:(109 - 3.11, 109 + 3.11) = (105.89, 112.11)

Upper Bound = 105.89

Lower Bound = 112.11

Part(d):

If the population was not Normal then we could not compute the confidence interval as the distribution is unknown.