Question

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

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.

Homework Answers

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

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