Question

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.

Answer 1

`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`