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Question Workspace Check My Work (2 remaining) The USA Today 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 $135.67, and the average expenditure in a sample survey of 30 female consumers was $68.64. Based on past surveys, the standard deviation for male consumers is assumed to be $38, and the standard deviation for female consumers is assumed to be $19.

A. What is the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females (to 2 decimals)?

B. At 99% confidence, what is the margin of error (to 2 decimals)?

C. Develop a 99% confidence interval for the difference between the two population means (to 2 decimals). Use z-table. ( __,__ )

Answer #1

The statistical software output for this problem is:

**Two sample Z summary confidence interval:**

μ_{1} : Mean of population 1 (Std. dev. = 38)

μ_{2} : Mean of population 2 (Std. dev. = 19)

μ_{1} - μ_{2} : Difference between two means

**99% confidence interval results:**

Difference | n1 | n2 | Sample mean | Std. err. | L. limit | U. limit |
---|---|---|---|---|---|---|

μ_{1} -
μ_{2} |
40 | 30 | 67.03 | 6.9378191 | 49.159362 | 84.900638 |

Hence,

a) Point estimate = **67.03**

b) Margin of error = (84.90 - 49.16)/2 =
**17.87**

c) 99% confidence interval:

(**49.16**, **84.90**)

Question Workspace
Check My Work
The USA Today 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 $135.67, and the average expenditure in a
sample survey of 30 female consumers was $68.64. Based on past
surveys, the standard deviation for male consumers is assumed to be
$35, and the standard deviation for female consumers is assumed...

The USA Today 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 43 male consumers was $135.67, and the average expenditure in a
sample survey of 37 female consumers was $68.64. Based on past
surveys, the standard deviation for male consumers is assumed to be
$36, and the standard deviation for female consumers is assumed to
be $18.
What is...

The USA Today
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 44 male consumers was
$135.67, and the average expenditure in a sample survey of 37
female consumers was $68.64. Based on past surveys, the standard
deviation for male consumers is assumed to be $36, and the standard
deviation for female consumers is assumed to be $20.
At 99%...

The USA Today 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 $135.67, and the average expenditure in a
sample survey of 32 female consumers was $68.64. Based on past
surveys, the standard deviation for male consumers is assumed to be
$31, and the standard deviation for female consumers is assumed to
be $16.
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The USA Today 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 44 male consumers was $135.67, and the average expenditure in a
sample survey of 31 female consumers was $68.64. Based on past
surveys, the standard deviation for male consumers is assumed to be
$32, and the standard deviation for female consumers is assumed to
be $18.
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the amounts they spend? The average expenditure in a sample survey
of 49 male consumers was $135.67, and the average expenditure in a
sample survey of 32 female consumers was $68.64. Based on past
surveys, the standard deviation for male consumers is assumed to be
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sample survey of 35 female consumers was $68.64. Based on past
surveys, the standard deviation for male consumers is assumed to be
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be $19.
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The USA Today 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 $135.67, and the average expenditure in a
sample survey of 30 female consumers was $68.64. Based on past
surveys, the standard deviation for male consumers is assumed to be
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The USA Today 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
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sample survey of 34 female consumers was $68.64. Based on past
surveys, the standard deviation for male consumers is assumed to be
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be $24.
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