Question

The Eagle Ridge Contractors Association claims the average price of a home in their subdivision is $130,000 with a standard deviation of $7,000. A sample of 16 homes for sale in this subdivision had an average selling price of $125,550. The Eagle Ridge Home Owners Association is interested in knowing if the costs of homes for sale in this subdivision are actually lower than claimed. Assuming that the costs of homes are normally distributed, what is the p-value for this test?

Answer 1

n=16,  = 130000,  

= 125550  , = 7000

a)

Here we know the population standard deviation ( )

hence, we are using Z Test

null and alternative hypothesis is

Ho:   = 130000

H1:   < 130000

formula for test statistics is

z = -2.5429

test statistics= -2.54

calculate P-Value

P-Value = P(z < -2.54)

using normal z table we get

P(z < -2.54) = 0.0055

P-Value = 0.0055