Question

Do women feel differently from men when it comes to tax​ rates? One question on a survey of randomly selected adults​ asked, "What percent of income do you believe individuals should pay in income​ tax?" Complete the following

Gender	Tax Rate	Gender	Tax Rate
Female	10	Male	15
Female	10	Male	20
Female	6	Male	8
Female	23	Male	10
Female	20	Male	17
Female	15	Male	2
Female	8	Male	1
Female	15	Male	15
Female	3	Male	2
Female	5	Male	8
Female	25	Male	15
Female	10	Male	5
Female	0	Male	16
Female	19	Male	33
Female	10	Male	10
Female	0	Male	15
Female	8	Male	2
Female	20	Male	0
Female	14	Male	4

	Female	13	Male	6
	Female	20	Male	15
	Female	15	Male	5
	Female	9	Male	10
	Female	15	Male	5
	Female	5	Male	10
	Female	14	Male	22
	Female	15	Male	15
	Female	5	Male	16
	Female	16	male	8

Female

25

Male

10

Test whether the mean tax rate for females differs from that of males at the α=0.01 level of significance. Let

μM represent the mean income tax rate for males and let μF represent the mean income tax rate for females.

The null and alternative hypotheses for this test is

Ho: μM = μF

H1​μM ≠ μF

Find t 0, the test statistic for this hypothesis test.

t 0=

​(Round to two decimal places as​ needed.)

Answer 1

Solution:

The null and alternative hypothesis are:

To find the test statistic for this hypothesis test, we can use the excel data analysis tool. The excel output is given below:

t-Test: Two-Sample Assuming Equal Variances
	Tax Rat_Male	Tax Rate_Female
Mean	10.6667	12.4333
Variance	53.1954	47.3575
Observations	30	30
Pooled Variance	50.2764
Hypothesized Mean Difference	0
df	58
t Stat	-0.96
P(T<=t) one-tail	0.1693
t Critical one-tail	1.6716
P(T<=t) two-tail	0.3386
t Critical two-tail	2.0017

Therefore, the test statistic is: