Property taxes are based on assessed values of property. In most states, the law requires that assessed values be €œat or near€ market value of the property. In one Washington county, a tax protest group has claimed that assessed values are higher than market values. To address this claim, the county tax assessor, together with representatives from the protest group, has selected 15 properties at random that have sold within the past six months. Both parties agree that the sales price was the market value at the time of the sale.
The assessor then listed the assessed values and the sales values side by side, as shown.

a. Assuming that the population of assessed values and the population of market values have the same distribution shape and that they may differ only with respect to medians, state the appropriate null and alternative hypotheses.
b. Test the hypotheses using an α = 0.01 level.
c. Discuss why one would not assume that the samples were obtained from normal distributions for this problem. What characteristic about the market values of houses would lead you to conclude that these data were not normally distributed?

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House Assessed Value ( Market Value ($) 302,000 176,000 149.000 198.500 214.000 235,000 305,000 187.500 150,000 223,000 178,500 245,000 167,000 219,000 334,000 198,000 182.400 154.300 198.500 218.000 230,000 298,900 190,000 149,800 222.000 180,000 250,900 165,200 220,700 320,000 10 12 13 14 15