The average price for new mobile homes is known to be distributed with population standard deviation...

The average price for new mobile homes is known to be distributed with population standard deviation of 300. If a random sample of 36 homes resulted in a sample mean of 55, 000, obtain a 90% confidence interval.

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 55000

Population standard deviation = = 300

Sample size = n = 36

At 90% confidence level

= 1-0.90% =1-0.90 =0.10

/2 =0.10/ 2= 0.05

Z/2 = Z_0.05 = 1.645

Z/2 = 1.645

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

= 1.645* ( 300 / $\sqrt$ 36 )

= 82.24

At 90 % confidence interval estimate of the population mean is,

- E < < + E

55000 - 82.24 < < 55000 + 82.24

54917.76 < < 55082.24

( 54917.76 ,55082.24 )

orchestra answered 1 year ago

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