Question

The mean time taken to design a house plan by 38 architects was found to be 19 hours with a standard deviation of 3.25 hours.

Construct a 95% confidence interval for the population mean μ.


Round your answers to two decimal places.

_______to_________ hours

b. Suppose the confidence interval obtained in part a is too wide. Select all of the ways the width of this interval can be reduced.

Lowering the confidence level

Increasing the confidence level

Lowering the sample size

Increasing the sample size

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 19

Population standard deviation =    = 3.25

Sample size n =38

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 1.96 * ( 3.25/ 38 )

= 1.03
At 95% confidence interval estimate of the population mean
is,

- E < < + E

19 - 1.03 <   < 19+ 1.03

17.97 <   < 20.03
( 17.97 , 20.03 )