Question

Using the following data below, answer parts a-b. 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?" Test whether the mean tax rate for females differs from that of males at the a=0.01 level of significance.

A) Find the test statistic for this hypothesis test.

B) Determine the​ P-value for this test.

Data:

Gender	Tax Rate	Gender	Tax Rate
Female	10	Male	15
Female	10	Male	20
Female	6	Male	10
Female	19	Male	10
Female	20	Male	17
Female	15	Male	2
Female	8	Male	1
Female	15	Male	15
Female	3	Male	4
Female	5	Male	10
Female	25	Male	15
Female	10	Male	5
Female	0	Male	15
Female	19	Male	35
Female	10	Male	10
Female	0	Male	15
Female	8	Male	2
Female	20	Male	0
Female	14	Male	4
Female	12	Male	6
Female	20	Male	15
Female	15	Male	6
Female	9	Male	10
Female	16	Male	6
Female	5	Male	10
Female	16	Male	23
Female	15	Male	15
Female	5	Male	17
Female	18	Male	8
Female	25	Male	10

Answer 1

Solution:

Here, we have to use two sample t test for the difference in the population means assuming equal population variances.

The null and alternative hypotheses for this test are given as below:

Null hypothesis: H₀: the mean tax rate for females do not differs from that of males.

Alternative hypothesis: H_a: the mean tax rate for females differs from that of males.

H₀: µ₁ = µ₂ versus H_a: µ₁ ≠ µ₂

µ₁ = mean tax rate for females

µ₂ = mean tax rate for males

This is a two tailed test.

We are given

Level of significance = α = 0.01

(Part A)

Test statistic formula for pooled variance t test is given as below:

t = (X1bar – X2bar) / sqrt[S_p²*((1/n1)+(1/n2))]

Where S_p² is pooled variance

S_p² = [(n1 – 1)*S1^2 + (n2 – 1)*S2^2]/(n1 + n2 – 2)

From given data, we have

X1bar = 12.43333

X2bar = 11.03333

S1 = 6.795959

S2 = 7.41147

n1 = 30

n2 = 30

df = n1 + n2 – 2 = 30 + 30 – 2 = 58

S_p² = [(n1 – 1)*S1^2 + (n2 – 1)*S2^2]/(n1 + n2 – 2)

S_p² = [(30 – 1)* 6.795959^2 + (30 – 1)* 6.795959^2]/(30 + 30 – 2)

S_p² = 50.5575

t = (X1bar – X2bar) / sqrt[S_p²*((1/n1)+(1/n2))]

t = (12.43333 – 11.03333) / sqrt[50.5575*((1/30)+(1/30))]

t = 0.7626

(Part B)

P-value = 0.4488

(by using t-table)

P-value > α = 0.01

So, we do not reject the null hypothesis

There is insufficient evidence to conclude that the mean tax rate for females differs from that of males at the α = 0.01 level of significance.