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.

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One question on a survey of randomly selected adults asked, "What
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Gender
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10
Male
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10
Male
20
Female
6
Male
8
Female
23
Male
10
Female
20
Male
17
Female
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Male
2
Female
8
Male
1
Female
15
Male
15
Female
3
Male
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