Question

A survey of 25 randomly selected customers found the ages shown​ (in years). The mean is 32.52 years and the standard deviation is 9.40 years. ​

37	33	38	24	48
41	39	38	15	26
20	41	37	25	11
28	35	33	28	31
40	30	48	42	25

a) Construct a 99​% confidence interval for the mean age of all​ customers, assuming that the assumptions and conditions for the confidence interval have been met. (__,__)

​b) How large is the margin of​ error?

​c)

​c) What is the confidence interval using the given population standard​ deviation? Select the correct choice below and fill in the answer boxes within your choice.

​(Round to two decimal places as​ needed.)

A.The new confidence interval ​(__,__) is wider than the interval from part a.

B.The new confidence interval ​(__,__) (__,__) is narrower  than the interval from part a.

Answer 1

a) 99% confidence interval for mean =

here 2.80 is the critical value or t value for 99% interval at n-1 degrees of freedom which is 24 d.f

therefore, the 99% C.I=

= =

b) The margin of error =

= = 5.26

c) Using the given population sd the confidence interval is =

= (27.7,37.4)

Thus option B is correct the new C.I is narrower than part a