Please answer Part B The crisis in the real estate market caused the listing pri

Question

Please answer Part B

The crisis in the real estate market caused the listing prices of homes in certain areas to fall from previous years. A real estate office would like to sample 54 new listings randomly to test the hypothesis that the current listing price average is less than $244,000, the average in the previous year. Assume the standard deviation for the price of homes in this market is $46,000. Complete parts a through d below. a. Explain how Typo I and Type II errors can occur in this hypothesis test. A Type I error can occur if the average listing price is above or equal to $244,000 and the null hypothesis is rejected. A Type II error can occur if the average listing price is below $244,000 and the null hypothesis is not rejected. b. Using a = 0.10, calculate the probability of a Type II error occurring if the actual average listing is $225,000. The probability of committing a Type II error is (Round to three decimal places as needed.)

Explanation / Answer

b) here std error =std deviaiton/(n)1/2 =6259.807

for 0.1 level of significance criitical z =-1.2816

therefore critical region =mean +z*std error =244000-1.2816*6259.807=235977.7344

therefore type II error =P(X>235977.7344) =1-P(X<235977.7344)=1-P(X<(235977.7344-225000)/6259.807)

=1-P(Z<1.7537)=1-0.9603 =0.0397 ~0.040

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