Question

You may need to use the appropriate appendix table or technology to answer this question.

A newspaper reports that the average expenditure on Valentine's Day is $100.89. Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of 40 male consumers was $138.67, and the average expenditure in a sample survey of 30 female consumers was $61.64. Based on past surveys, the standard deviation for male consumers is assumed to be $35, and the standard deviation for female consumers is assumed to be $20.

(a)

What is the point estimate (in dollars) of the difference between the population mean expenditure for males and the population mean expenditure for females? (Use male − female.)

$

(b)

At 99% confidence, what is the margin of error (in dollars)? (Round your answer to the nearest cent.)

$

(c)

Develop a 99% confidence interval (in dollars) for the difference between the two population means. (Use male − female. Round your answer to the nearest cent.)

$ to $

Answer #1

x_{1}
= |
138.67 |
x_{2}
= |
61.64 |

n_{1}
= |
40 |
n_{2}
= |
30 |

σ_{1}
= |
35.00 |
σ_{2}
= |
20.00 |

a)

Point estimate of differnce '=x1-x2 = | 77.03 |

b)

std error
σ_{}_{1-}_{}_{2}=√(σ^{2}1/n_{1}+σ^{2}_{2}/n_{2})
= |
6.630 |

for 99 % CI value of z= | 2.576 | ||

margin of error E=z*std error = |
17.09 |

c)

lower bound=(x1-x2)-E = | 59.952 | ||

Upper bound=(x1-x2)+E = | 94.108 | ||

from above
99% confidence interval for population mean =(59.95 to
94.11) |

You may need to use the appropriate appendix table or technology
to answer this question.
A newspaper reports that the average expenditure on Valentine's
Day is $100.89. Do male and female consumers differ in the amounts
they spend? The average expenditure in a sample survey of 40 male
consumers was $137.67, and the average expenditure in a sample
survey of 30 female consumers was $65.64. Based on past surveys,
the standard deviation for male consumers is assumed to be $45,...

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they spend? The average expenditure in a sample survey of 40 male
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the standard deviation for male consumers is assumed to be $35, and
the standard deviation for female consumers is assumed to be
$20.
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