5- Laura is thinking about buying a house which is listed for $520,000. The realtor tells her that the house is listed below the average price of similar houses in the neighbourhood. So, she is thinking about buying the house and selling it quickly for a profit. Laura is facing this hypothesis testing problem

{ ₀: = $520,000 ( )

{ : > $520,000 ()

where is the true average of the prices of similar houses in that neighbourhood.

(A) Describe Type I error in the context of this question and explain its consequences to Laura.

(B) Describe Type II error in the context of this question and explain its consequences to Laura.

(C) The realtor shows Laura the sale prices of 32 similar houses in the neighbourhood which on average were sold for $562,000 with standard deviation of $63,000. Based on this data, at = 0.05, should Laura buy the house or not? Explain.

6- The areas covered by one gallon paint cans of certain brand are normally distributed. We purchased 8 of them from 8 different stores to maintain the randomness of our sample. We measured the coverage area each one gave. The coverages in square feet are as follows

344.3, 288.1, 328.7, 293.4, 374.6, 350.1, 325.1, 368.9

Construct a 95% confidence interval for the true average of coverage area of one gallon paint cans of this brand.