It is claimed that the median increase in home owners taxes in a certain county

Question

It is claimed that the median increase in home owners taxes in a certain county is 300$. A random sample of 20 home owners gives the following tax-increase data (arranged from smallest to largest): 137, 143, 176, 188, 195, 209, 211, 228, 233, 241, 26, 279, 285, 296, 312, 329, 342, 357, 412, 517. (a). Does the data present strong enought evidence to conclude that the claim is false? State the null and alternative hypothesis and test at a level a=0.05. (b). Does the data present strong enough evidence to conclude that the median increase is less than 300? Test at level a=0.05.

Explanation / Answer

we will use minitab software for this problem and we use nonparamertic ine sample sign rank test

a) we set hyppthesis as

H0: meadian=300 H1: median<300

b) result at significance 0.05

Sign Test for Median:

Sign test of median = 300.0 versus < 300.0

N Below Equal Above P-value Median
20 14 0 6 0.0577 237.0

since p-value=0.0577 > 0.05

we accept H0 and c;aim that the sample median reaches to 300

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