The dataset HomesForSale has data on houses available for sale in the Mid-Atlantic states (NY, NJ, and PA). For a random sample of 30 houses in New York, the mean is = 565.5, in thousands of dollars, with standard deviation, s = 697.6. Use this data, a 5% significance level, and the knowledge that within the U.S. the average house sells for about 265 thousand dollars to test whether the average cost of a house in New York is greater than the U.S. average.

a. State the hypotheses for this test. Use correct notation and define the parameter in a complete sentence for full credit.

b. Calculate the test statistic. Show work for full credit. Round to two decimal places.

c. Use the appropriate theoretical distribution in StatKey to find the p-value. Include a sketch or StatKey image of your distribution for full credit.

d. State the formal decision for this test if we assume a 5% significance level: Reject Null Hypothesis or Do Not Reject Null Hypothesis.

e. State the conclusion of this test in context, in a complete sentence, with correct units.