Question

Use the following for questions 2 and 3. A simple random sample of 30 items was selected. The sample mean was 15 and the population standard deviation is known to be 6. What is a 90% confidence interval for the population mean?

Is it reasonable to conclude that the population mean could 14?

Yes, because 14 is in the confidence interval

Yes, because 14 is not in the confidence interval

No, because 14 is in the confidence interval

No, because 14 is not in the confidence interval

Answer 1

Solution:

Note that, Population standard deviation() is known. So we use z distribution.

Our aim is to construct 90% confidence interval.

c = 0.90

= 1- c = 1- 0.90 = 0.10

  /2 = 0.10 2 = 0.05 and 1- /2 = 0.950

Search the probability 0.950 in the Z table and see corresponding z value

  = 1.645   

The margin of error is given by

E =  /2 * ( / n )

= 1.645 * (6 / 30)

= 1.802

Now , confidence interval for mean() is given by:

( - E ) <   <  ( + E)

(15 - 1.802)   <   <  (15 + 1.802)

13.198 <   < 16.802

(13.198 , 16.802 )

Is it reasonable to conclude that the population mean could 14?

Yes, because 14 is in the confidence interval