Question

​c) Test whether the mean tax rate for females differs from that of males at the

alpha=0.10 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.

Upper H0: μM = μF

versus

Upper H1​: μM ≠ μF

Find t0 the test statistic for this hypothesis test.

Gender   Tax Rate   Gender   Tax Rate
Female   10   Male   15
Female   10   Male   20
Female   4   Male   10
Female   19   Male   10
Female   20   Male   17
Female   15   Male   2
Female   10   Male   1
Female   15   Male   15
Female   3   Male   3
Female   5   Male   8
Female   23   Male   15
Female   10   Male   5
Female   0   Male   16
Female   20   Male   34
Female   10   Male   10
Female   0   Male   15
Female   7   Male   2
Female   20   Male   0
Female   14   Male   4
Female   14   Male   5
Female   20   Male   15
Female   15   Male   6
Female   9   Male   10
Female   15   Male   5
Female   5   Male   10
Female   14   Male   22
Female   15   Male   15
Female   5   Male   17
Female   18   Male   8
Female   25   Male   10

Answer 1

Using Excel, go to Data, select Data Analysis, choose t-Test: Two-Sample Assuming Unequal Variances at alpha = 0.1.

	Female	Male
Mean	12.33333	10.83333
Variance	45.47126	54.35057
Observations	30	30
Hypothesized Mean Difference	0
df	58
t Stat	0.822317
P(T<=t) one-tail	0.207132
t Critical one-tail	1.296319
P(T<=t) two-tail	0.414265
t Critical two-tail	1.671553

H0: μM = μF

H1: μM ≠ μF

Test statistic = 0.822

p-value = 0.414

Since p-value is more than 0.1, we do not reject the null hypothesis and conclude that μM = μF

So, mean tax rate for females does not differe from that of males.