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A sociologist wishes to see if it is true that for a certain group of professional women, the average age at which they have their first child is 28.6 years. A random sample of 36 women is selected, and their ages at the birth of their first child are recorded. At α = 0.05, does the evidence refute the sociologist’s assertion? Assume σ = 4.18.

Respuesta :

Answer:

[tex]Z = 2.1\ is\ higher\ than\ 1.96, we\ reject\ H_o[/tex]

Step-by-step explanation:

The explanation of given question is described below:

Here, the test of hypothesis states that

[tex]H_o : Mean = 28.6[/tex]

[tex]H_a : Mean\ which\ is\ not\ equals\ 28.6[/tex]

The test statistic is

[tex]Z = \frac{(\bar X - Mean)}{\frac{Population\ standard\ deviation}{vn} }[/tex]

[tex]Z = \frac{(30.06 - 28.6)}{\frac{4.18}{6} }[/tex]

= 2.1

According to the given data α = 0.05,

So, the major value is

[tex]IZ(0.025)I = 1.96[/tex]

(refer to the standard normal table) .

Finally

[tex]Z = 2.1\ is\ higher\ than\ 1.96, we\ reject\ H_o[/tex]

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