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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.

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Answer:


Z = 2.1\ is\ higher\ than\ 1.96, we\ reject\ H_o

Explanation:

The explanation of given question is described below:

Here, the test of hypothesis states that


H_o : Mean = 28.6


H_a : Mean\ which\ is\ not\ equals\ 28.6

The test statistic is


Z = ((\bar X - Mean))/((Population\ standard\ deviation)/(vn) )


Z = ((30.06 - 28.6))/((4.18)/(6) )

= 2.1

According to the given data α = 0.05,

So, the major value is


IZ(0.025)I = 1.96

(refer to the standard normal table) .

Finally


Z = 2.1\ is\ higher\ than\ 1.96, we\ reject\ H_o

User Thomas Lann
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