Question

In: Statistics and Probability

300 air conditioners were tested and it was found that the average power usage per hour...

300 air conditioners were tested and it was found that the average power usage per hour during the summer months (for around 9 hours per day) is 4200 W. Find the 95% confidence interval if sigma = 100 W.

Expert Solution

Solution :

Given,

= 4200

= 100

n = 300

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

Our aim is to construct 95% confidence interval.

c = 0.95

= 1- c = 1- 0.95 = 0.05

/2 = 0.05 2 = 0.025 and 1- /2 = 0.975

Search the probability 0.975 in the Z table and see corresponding z value

= 1.96

The margin of error is given by

E = /2 * ( / n )

= 1.96 * ( 100/ 300 )

= 11.316

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

( - E ) < < ( + E)

( 4200 - 11.316 ) < < ( 4200 + 11.316 )

4188.684 < < 4211.316

Required 95% confidence interval is ( 4188.684 , 4211.316 )

orchestra answered 2 years ago

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