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lapo4ka
1 month ago
12

A sociologist wishes to see if it is true that for a certain group of professional women, the average age at which they have the

ir 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.
Mathematics
1 answer:
babunello [11.8K]1 month ago
3 0

Response:

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

Clarification:

The explanation for the provided question is outlined below:

The hypothesis test indicates that

H_o: Mean = 28.6

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

The test statistic calculated is

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

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

= 2.1

As per the given information, α = 0.05,

Thus, the critical threshold is

IZ(0.025)I = 1.96

(as per the standard normal table).

Summarily

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

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