Question
Asked Dec 12, 2019
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Please answer number 13. 

13) A 1970 study showed that of American married-couple families, 43% had no children, 18%
had one child, 18% had two children and 21% had three or more children. A recent survey of
500 American married-couple families revealed that 267 had no children, 87 had one child, 96
had two children and 50 had three or more children. At the 0.01 level of significance, test the
claim that the 1970 proportions are no longer valid.
MacBook Air
FIL
F10
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13) A 1970 study showed that of American married-couple families, 43% had no children, 18% had one child, 18% had two children and 21% had three or more children. A recent survey of 500 American married-couple families revealed that 267 had no children, 87 had one child, 96 had two children and 50 had three or more children. At the 0.01 level of significance, test the claim that the 1970 proportions are no longer valid. MacBook Air FIL F10

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Expert Answer

Step 1

It is given that 43% had no children, 18% are had one child, 18% are have two children, 21% have three or more children.

The null and alternative hypotheses are stated below:

H0: P1= 0.43, P2= 0.18, P3= 0.18, P4= 0.21.

Ha: P1≠ 0.43, P2≠ 0.18, P3≠ 0.18, P4 ≠0.21.

The chi-square test is appropriate in this situation.

The test statistic is given below:

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The test statistic is given below: (0,- E.) (k-1) E Where: O, = Observed frequency E = Expected frequency k = Number of observations

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Step 2

The Expected frequencies and test statis...

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Oi Ei (Oi-Ei)^2/Ei 267 215(=500×0.43) 90(=500x0.18) No children 12.5767 1 Child 87 0.1000 90(=500x0.18) 0.4000 2 children 96 105(=500x0.21) 3 or more children 50 28.8095 500 Total 500 41.8862

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