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A school in New Zealand collected data about the employment status of the mother and father in two-parent families. The two-way table of column relative frequencies below shows the data.
Father works full time Father works part time Father not working
Mother works full time
0.17
0.170, point, 17
0.14
0.140, point, 14
0.13
0.130, point, 13
Mother works part time
0.23
0.230, point, 23
0.14
0.140, point, 14
0.07
0.070, point, 07
Mother not working
0.60
0.600, point, 60
0.71
0.710, point, 71
0.80
0.800, point, 80
Column total
1.00
1.001, point, 00
1.00
1.001, point, 00
1.00
1.001, point, 00
Based on the data, which of the following statements must be true for the two-parent families at that school?
Choose 1 answer:
Choose 1 answer:

(Choice A)
A
A family where the father works part time is twice as likely as a family where the father is not working to have the mother work part time.

(Choice B)

It is most common for neither parent to be working.

(Choice C)
C
Families where the father works full time are more likely to have the mother working full time than part time.

(Choice D)
D
There are twice as many families where the mother works full time and the father works part time as families where the mother works part time and the father doesn't work.

Answer :

Answer:A

Step-by-step explanation: 14% of the mothers work part-time in families where the father works part-time while 7% of the mothers work part-time in families where the father is not working.

MrRoyal

Probabilities are used to determine how likely or unlikely an event is. From the 2-column table, it is twice as likely to get a family where the father and the mother work part-time than a family where the father doesn't work, and the mother works part-time.

We use the following representation:

[tex]FF \to[/tex] Father works full-time

[tex]FP \to[/tex] Father works part-time

[tex]FW \to[/tex] Father not working

[tex]MF \to[/tex] Mother works full-time

[tex]MP \to[/tex] Mother works part-time

[tex]MW \to[/tex] Mother not working

Next, we test each of the 4 options, till one of the options is true (see attachment)

Choice A:

The claim in choice A is that:

[tex]P(FP\ and\ MP) = 2 \times P(FW\ and\ MP)[/tex]

From the given table, we have:

[tex]P(FP\ and\ MP) = 0.14[/tex] ---- father works part-time and mother works part-time

[tex]P(FW\ and\ MP) =0.07[/tex] ---- father not working and mother works part-time

Put the above values in the following equation

[tex]P(FP\ and\ MP) = 2 \times P(FW\ and\ MP)[/tex]

[tex]0.14 = 2 \times 0.07[/tex]

[tex]0.14 = 0.14[/tex]

The above equation is true.

Hence, choice (A) is true

Read more about probabilities at:

https://brainly.com/question/24297863

${teks-lihat-gambar} MrRoyal

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