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lapo4ka
6 days 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 [11.3K]6 days 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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Answer:

C. The hypotenuse measures twice the distance of the shorter leg.

B. The longer leg is √3 times the length of the shorter leg.

Step-by-step explanation:

A 30-60-90 triangle is considered a right triangle. Triangles containing a right angle are classified as right triangles. Only one right angle can exist in such a triangle. The representation of this case is illustrated below. Let’s clarify why the proposed statements are valid:

The hypotenuse of a right triangle is always opposite to the right angle. If we designate a as the shorter leg, the sine law affirms that the hypotenuse is:

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This indicates that the hypotenuse is double the length of the shorter leg

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H^2=x^2+a^2 \\ \\ x=\sqrt{H^2-a^2} \\ \\ x=\sqrt{(2a)^2-a^2} \\ \\ x=\sqrt{4a^2-a^2} \\ \\ x=\sqrt{3a^2}=\sqrt{3}a

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9 days ago
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