Question

In: Statistics and Probability

The mean time taken to design a house plan by 39 architects was found to be...

The mean time taken to design a house plan by 39 architects was found to be 17 hours with a standard deviation of 3.25 hours.

Construct a 98% confidence interval for the population mean μ.

Round your answers to two decimal places.

_____to_____ hours

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 17

Population standard deviation = = 3.25

Sample size = n =39

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

Z/2 = Z0.01 = 2.326 ( Using z table )

Margin of error = E = Z/2 * ( / $\sqrt$ n)

= 2.326 * ( 3.25/ $\sqrt$ 39)

=1.21
At 98% confidence interval

- E < < + E

17- 1.21 < < 17+1.21

15.79 to 18.21

orchestra answered 2 years ago

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