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 parts​ a) through​ c).

Gender   Tax Rate   Gender   Tax Rate
Female   10   Male   15
Female   10   Male   20
Female   4   Male   10
Female   21   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   8
Female   23   Male   15
Female   10   Male   5
Female   0   Male   16
Female   19   Male   33
Female   10   Male   10
Female   0   Male   15
Female   7   Male   2
Female   20   Male   0
Female   14   Male   4
Female   13   Male   7
Female   20   Male   15
Female   15   Male   6
Female   9   Male   10
Female   14   Male   6
Female   5   Male   10
Female   13   Male   23
Female   15   Male   15
Female   5   Male   15
Female   17   Male   8
Female   23   Male   10

​c) Test whether the mean tax rate for females differs from that of males at the alphaαequals=0.01 level of significance.

Determine the null and alternative hypotheses for this test. Let μM represent the mean income tax rate for males and let μF represent the mean income tax rate for females.

d) Find t0​, the test statistic for this hypothesis test.

Answer 1

Ho :
Ha :

Level of significance (l.o.s.) : = 0.01

Test Statistics : t-Test: Two-Sample Assuming Equal Variances ( Student's t distribution is used since population variances are unknown )

Decision Criteria : Reject Ho at 1% l.o.s. if | to | > t tab,
where t tab = t(/2, n-1) = t( 0.005, 58) = 2.6633

Calculations : The results for this test is obtained using MS-Excel and for this, following steps are needed to be followed :

Step 1 : Enter the data in excel.
Step 2 : Select the "t-Test: Two-Sample Assuming Equal Variances" function available in the data analysis package under the data tab in MS-Excel.
Step 3 : Enter the range of the female tax rates in the first cell and that of male tax rates in the second cell.
Step 4 : Change the default l.o.s. from 0.05 to 0.01 and then press ok. Following results would be obtained :

t-Test: Two-Sample Assuming Equal Variances
	Males	Females
Mean	10.9	12.1
Variance	51.33448276	44.16206897
Observations	30	30
Pooled Variance	47.74827586
Hypothesized Mean Difference	0
df	58
t Stat	-0.672586318
P(T<=t) one-tail	0.25194069
t Critical one-tail	2.392377475
P(T<=t) two-tail	0.50388138
t Critical two-tail	2.663286954

Thus, to = t Stat = -0.672586318

Conclusion : SInce | to | < t tab, we do not reject Ho at 1% l.o.s. and thus, conclude that the mean tax rate for females does not differs significantly from that of males.

Hope this answers your query!