Mathematics, 16.10.2020 14:01 thao5160
The changes in housing prices over short time periods are in part determined by supply and demand. A real estate company in Minnesota projected an increase in its average selling prices of homes in the first quarter of 2014 over the mean 2013 selling price of $201,800. The reason for the projection was an increase in demand due to business expansion and the subsequent increase in labor. To investigate the accuracy of the projection, a sample of homes in the first quarter of 2014 was selected and the following selling prices (in $) recorded:
235,000 271,900 183,300 203,000 182,900 225,500 189,000 214,200 237,900 233,500 217,000 230,400 202,950, 216,500 209,900, 245,500
Required:
a. At 5% level of significance, is there sufficient evidence to support the real estate company's projection?
b. Which statistical distribution should be applied in this situation and why? Explain carefully.
c. Discuss the consequences of Type I and Type II errors in terms of the problem.
d. Does the management at the real estate company want a small or large value of the significance level? Explain carefully.
e. Based on a 95% confidence level, estimate the actual average selling price homes in the first quarter of 2014.
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