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

Answer:

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

Step-by-step 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

$Z = \frac{(\bar X - Mean)}{\frac{Population\ standard\ deviation}{vn} }$

$Z = \frac{(30.06 - 28.6)}{\frac{4.18}{6} }$

= 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

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