A tax collector wishes to see if the mean values of the tax-exempt properties ar

Question

A tax collector wishes to see if the mean values of the tax-exempt properties are different for two cities. The values of the tax-exempt properties for the two samples are shown. The data are given in millions of dollars. At a = 0.02. is there enough evidence to support the tax collector's claim that the means are different? Use mu_1 for the mean value of tax-exempt properties in City A. Assume the variables are normally distributed and the variances are unequal. State the hypotheses and identify the claim with the correct hypothesis.

Explanation / Answer

Solution:

For the given two sample t test for the population means, the null and alternative hypotheses are given as below:

Null hypothesis:

H0: µ1 - µ2 = 0

Alternative Hypothesis:

H0: µ1 - µ2 0

This hypothesis test is two tailed test.

(If alternative hypothesis consist of ‘<’, then it is one tailed - left tailed, ‘>’ indicate one tailed – right tailed and ‘’ indicate two tailed or non-directional test.)

From the given data, we have

Level of Significance

0.05

Population 1 Sample

Sample Size

12

Sample Mean

25

Sample Standard Deviation

11.9164

Population 2 Sample

Sample Size

10

Sample Mean

54.5

Sample Standard Deviation

12.6951

Degrees of freedom = 18

Test statistic = t = (X1bar – X2bar) / sqrt((s1^2/n1)+(S2^2/n2))

Test statistic = t = (25 - 54.5)/sqrt((11.9164^2/12)+( 12.6951^2/10))

Test statistic = t = -5.57996642

Lower Critical Value

-2.1009

Upper Critical Value

2.1009

p-Value

0.0000

P-value < level of significance

So, we reject the null hypothesis

There is sufficient evidence to conclude that means are different.

Level of Significance

0.05

Population 1 Sample

Sample Size

12

Sample Mean

25

Sample Standard Deviation

11.9164

Population 2 Sample

Sample Size

10

Sample Mean

54.5

Sample Standard Deviation

12.6951

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