Question

Tax exempt properties: A tax collector wishes to see if the mean values of the tax-exempt properties in two cities are different. Alpha= 0.02

City 1:  11,45,33,40,23,45,23,67,34,23,56

City2: 44,55,33,45,25,11,44,54,74,41,15

(Testing the means of two independent samples - t test)

Answer 1

Solution1:

Null hypothesis

Ho:

Alternative Hypothesis

Ha:

alpha=0.02

enter below R code to get the t statistic and p value

City_1 <- c( 11,45,33,40,23,45,23,67,34,23,56)

City_2 <- c( 44,55,33,45,25,11,44,54,74,41,15)
t.test(City_1,City_2,conf.level = 0.98)

Output:

   Welch Two Sample t-test

data: City_1 and City_2
t = -0.50228, df = 19.742, p-value = 0.621
alternative hypothesis: true difference in means is not equal to 0
98 percent confidence interval:
-22.50793 15.05338
sample estimates:
mean of x mean of y
36.36364 40.09091

t statistic=-0.50228

p value= 0.621

p>alpha

0.621>0.02

Fail to reject Ho.

Accept Ho.

Conclusion:

There is no sufficient statistical evidence at 2% level of significance to conclude that

the mean values of the tax-exempt properties in two cities are different.