Question

Could the number of cars owned be related to whether an individual has children? In a local town, a simple random sample of 200 residents was selected. Data was collected on each individual on how many cars they own and whether they have children. The data was then presented in the frequency table:

Number of Vehicles	Do you have children		Total
	No	Yes
Zero	24	50	74
One	27	25	52
Two or more	57	17	74
Total	108	92	200

Part A: What proportion of residents in the study have children and own at least one car? Also, what proportion of residents in the study do not have children and own at least one car? (2 points)

Part B: Explain the association between the number of cars and whether they have children for the 200 residents. Use the data presented in the table and proportion calculations to justify your answer. (4 points)

Part C: Perform a chi-square test for the hypotheses.

H0: The number of cars owned by residents of a local town and whether they have children have no association.
Ha: The number of cars owned by residents of a local town and whether they have children have an association.

What can you conclude based on the p-value? (4 points)

Answer 1

Part A)

P(Children and own at least one car) = P(children and one car) + P(Children and more cars)

P(children and one car) = number of individuals with children and one car / total number of individuals

P(children and one car) = 25/200

P(children and more cars) = 17/200

Total P(children and at least one car) = (25+17)/200 = 45/200

.

Part B)

The number of cars and presence of children in a family seem to be positively related, we can also verify if the two varaibles are independent or not using the multiplication rule of probability here

For example:

P(Children ) = 92/200

P(One car) = 52/200

P(children and one car) = 25/200

.

If these two variables are not associated then they must follow the rule:

P(children) * P(one car) = P(Children AND one car)

92/200 *52/200 is not equal to 25/200

Hence these two variables are associated

.

Part C)

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