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Answer:
Test statistic z=0.65
P-value=0.52
Fail to reject the null hypothesis.
Step-by-step explanation:
Here we have to perform a hypothesis test on the difference of proportions. We may want to answer if there is significant difference in the proportions of male and females.
The null and alternative hypothesis are:
The significance level is defined as 0.05.
The YES proportion for females is:
The YES proportion for males is:
The weighted average of p can be calculated as:
With this p, we estimate the standard deviation
The test statistic z can be calculated as:
We can calculate the p-value for z, taking into account is a two-sided test
The P-value (0.52) is greater than the significance level (0.05), so the effect is not significant. It failed to reject the null hypothesis.
We have enough evidence to conclude that the proportions that vote YES are different between genres.
Answer:
The building is 13.91 m tall
Step-by-step explanation:
The parameters given are;
Angle of elevation to the top of the building = 71°
Angle of depression to the bottom of the building = 26°
Height of the man = 2 m
Therefore, the sight of the man, the man's height, and the distance of the man from the building forms a triangle where:
The hypotenuse side = The sight of the man to the bottom of the building
Hence;
In ΔABC, A being at the eye level or head level of the man, B at the foot and C at the bottom of the building
∴ ∠A + Angle of depression to the bottom of the building = 90°
∠A = 90° - 26° = 64°
∠B = 90° and ∠C = 26° (Sum of angles in a triangle)
Distance of the man from the building = BC
Given that the angle of elevation to the top of the building = 71°, we have;
ΔAET
Where:
A is at the head level of the man,
E is the point on the building directing facing the man and
T is the top of the building
Hence AE = BC and ∡TAE = 71°
TE + AB= The height of the building
∴ TE = tan(71°) × 4.1 = 11.91 m
Hence the height of the building = 11.91 + 2 = 13.91 m.