An accountant wants to know if the property taxes paid by clients who live in the city are different from those who live in the county.The property taxes paid by five clients from the city (sample 1)and five clients from the county (sample 2)are shown below. The value of the test statistic is _____.
A) 10
B) 21
C) 34
D) 55

Question

An accountant wants to know if the property taxes paid by clients who live in the city are different from those who live in the county.The property taxes paid by five clients from the city (sample 1)and five clients from the county (sample 2)are shown below.  The value of the test statistic is _____.
A) 10 
B) 21 
C) 34 
D) 55

Quizplus · Accepted Answer

The appropriate statistical test to compare the means of two independent samples is the two-sample t-test. Given the small sample sizes (n=5), we need to assume that the population variances are equal. The test statistic can be calculated as follows:

t = (x1̄ - x2̄) / [s^2p * (1/n1 + 1/n2)]^(1/2)

where x1̄ and x2̄ are the sample means, s^2p is the pooled sample variance, and n1 and n2 are the sample sizes.

Using the data provided, we can calculate the sample means and variances as follows:

x1̄ = (2880 + 3200 + 2650 + 1950 + 3520) / 5 = 2840
s1^2 = [(2880 - 2840)^2 + (3200 - 2840)^2 + (2650 - 2840)^2 + (1950 - 2840)^2 + (3520 - 2840)^2] / 4 = 840400

x2̄ = (2150 + 1720 + 2980 + 2790 + 3160) / 5 = 2560
s2^2 = [(2150 - 2560)^2 + (1720 - 2560)^2 + (2980 - 2560)^2 + (2790 - 2560)^2 + (3160 - 2560)^2] / 4 = 955600

s^2p = [(n1 - 1) * s1^2 + (n2 - 1) * s2^2] / (n1 + n2 - 2) = 139.2 * 10^3

Plugging these values into the formula for the t-test, we get:

t = (2840 - 2560) / [139.2 * 10^3 * (1/5 + 1/5)]^(1/2) = 3.05

Using a two-tailed test with a significance level of 0.05 and 8 degrees of freedom (n1 + n2 - 2), the critical value of t is approximately 2.306. Since the calculated value of t (3.05) is greater than the critical value, we reject the null hypothesis that there is no difference in property taxes between the city and the county. Therefore, we can conclude that there is a statistically significant difference in property taxes paid by clients who live in the city and those who live in the county.

An Accountant Wants to Know If the Property Taxes Paid