Question

The six households below contain one mom, one dad, and either one or two children. The table below indicates the Census-assigned household number (for reference purposes; it is not used in this assignment), the number of children in the household, a two-child household indicator variable, and the number of hours the mom works in a typical week.

household |
Number kids |
Two kids |
Mom's work hours |

16761 |
2 |
1 |
0 |

24438 |
2 |
1 |
45 |

41729 |
2 |
1 |
0 |

42802 |
1 |
0 |
35 |

63528 |
1 |
0 |
40 |

148848 |
1 |
0 |
0 |

Here is your task: Carry out a difference in means test of the null hypothesis that moms with one child work the same number of hours as moms with two kids; in other words, the null hypothesis is that average work hours is the same in both types of households. To do this, you'll have to answer the following question:

A. What is the average female work hours among one-child households? What is the average female work hours among two-child households? What is the difference in means?

B. What is the estimated standard error of the difference in means? (Hint: you have to calculate the variance of work hours for each group and plug these values, along with the number of observations in each group, in the formula in MM Chapter 1, footnote 17. You then have to take the square root of a large number; if you are doing this by hand, an approximate value is fine, and you can use the following hint to help you: the square root of 361 is 19 and the square root of 400 is 20. )

C. What is the value of the test statistic?

D. Is the difference in means statistically different from zero? In other words, do you reject the null hypothesis of equal work hours? (Hint: if the absolute value of the test statistic is greater than 1.96 we reject the null and say the difference in means is statistically different from zero, or "statistically significant". Angrist and Pischke describe the critical value as "about two" but the number 1.96 is the precise value at which the cumulative standard normal distribution (this is a "bell shaped curve") has 2.5% of the area under the curve and to the right. Thus, 95% of the area is under the curve between -1.96 and 1.96, and so 1.96 is known as the critical value for a test at the 5% significance level.)

Answer #1

We suspect that the regression error variance might be larger
for household with two children than one. We estimate the budget
share equation by OLS separately for households with on and two
children. From the 489 households with one child, the sum of
squared residuals is 465.83. For the 789 households with two
children, the sum of squared residuals is 832.77. Test the null
hypothesis that there is no difference between the regression error
variances for these two groups, against...

The type of household for the U.S. population and for a random
sample of 411 households from a community in Montana are shown
below.
Type of
Household
Percent of
U.S.
Households
Observed
Number
of Households in
the Community
Married with children
26%
105
Married, no children
29%
120
Single parent
9%
28
One person
25%
91
Other (e.g., roommates, siblings)
11%
67
Use a 5% level of significance to test the claim that the
distribution of U.S. households fits the...

The type of household for the U.S. population and for a random
sample of 411 households from a community in Montana are shown
below.
Type of Household
Percent of U.S.
Households
Observed Number
of Households in
the Community
Married with children
26%
103
Married, no children
29%
118
Single parent
9%
34
One person
25%
90
Other (e.g., roommates, siblings)
11%
66
Use a 5% level of significance to test the claim that the
distribution of U.S. households fits the...

The type of household for the U.S. population and for a random
sample of 411 households from a community in Montana are shown
below.
Type of Household
Percent of U.S.
Households
Observed Number
of Households in
the Community
Married with children
26%
96
Married, no children
29%
113
Single parent
9%
32
One person
25%
97
Other (e.g., roommates, siblings)
11%
73
Use a 5% level of significance to test the claim that the
distribution of U.S. households fits the...

The type of household for the U.S. population and for a random
sample of 411 households from a community in Montana are shown
below.
Type of Household
Percent of U.S.
Households
Observed Number
of Households in
the Community
Married with children
26%
101
Married, no children
29%
110
Single parent
9%
32
One person
25%
97
Other (e.g., roommates, siblings)
11%
71
Use a 5% level of significance to test the claim that the
distribution of U.S. households fits the...

The type of household for the U.S. population and for a random
sample of 411 households from a community in Montana are shown
below.
Type of Household
Percent of U.S.
Households
Observed Number
of Households in
the Community
Married with children
26%
104
Married, no children
29%
112
Single parent
9%
32
One person
25%
97
Other (e.g., roommates, siblings)
11%
66
Use a 5% level of significance to test the claim that the
distribution of U.S. households fits the...

The type of household for the U.S. population and for a random
sample of 411 households from a community in Montana are shown
below.
Type of Household
Percent of U.S.
Households
Observed Number
of Households in
the Community
Married with children
26%
93
Married, no children
29%
127
Single parent
9%
35
One person
25%
88
Other (e.g., roommates, siblings)
11%
68
Use a 5% level of significance to test the claim that the
distribution of U.S. households fits the...

The type of household for the U.S. population and for a random
sample of 411 households from a community in Montana are shown
below.
Type of Household
Percent of U.S.
Households
Observed Number
of Households in
the Community
Married with children
26%
98
Married, no children
29%
118
Single parent
9%
38
One person
25%
91
Other (e.g., roommates, siblings)
11%
66
Use a 5% level of significance to test the claim that the
distribution of U.S. households fits the...

The type of household for the U.S. population and for a random
sample of 411 households from a community in Montana are shown
below.
Type of Household
Percent of U.S.
Households
Observed Number
of Households in
the Community
Married with children
26%
97
Married, no children
29%
119
Single parent
9%
35
One person
25%
95
Other (e.g., roommates, siblings)
11%
65
Use a 5% level of significance to test the claim that the
distribution of U.S. households fits the...

The type of household for the U.S. population and for a random
sample of 411 households from a community in Montana are shown
below.
Type of Household
Percent of U.S.
Households
Observed Number
of Households in
the Community
Married with children
26%
92
Married, no children
29%
120
Single parent
9%
29
One person
25%
101
Other (e.g., roommates,
siblings)
11%
69
Use a 5% level of significance to test the claim that the
distribution of U.S. households fits the...

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