A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current h
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Answer:
Step-by-step explanation:
Hello!
The objective is to compare if the average time that families live in Gotham and Metropolis, the real state company thinks the average time is less in Gotham than in Metropolis. There are two populations of interest and therefore two variables:
X₁: Time a family has lived in Gotham.
n₁= 100 families
X[bar]₁= 35 months
S₁= 900 days
X₂: Time a family has lived in Metropolis.
n₂= 150 families
X[bar]₂= 50 months
S₂= 1050 days
You are studying the population means of both variables, so you have to work using the distribution of the sample means:
If:
X[bar]₁~N(μ₁;σ₁²/n₁)
X[bar]₂~N(μ₂;σ₂²/n₂)
We can say that the difference between these both distributions will have the following distribution:
(X[bar]₁-X[bar]₂)~N(μ₁-μ₂;σ₁²/n₁+σ₂²/n₂)
The population variance for the difference between the two sample means is:
σ₁²/n₁+σ₂²/n₂
Since both σ₁² = σ₂² = σ² we can say that:
σ² (1/n₁+1/n₂)To study the difference between two normal populations with unknown bu equal population variances the distribution to use is:
The estimation of the standard error of the difference is:
Sa= 992.8423≅ 992.84
The standard error of the difference between the two sample means is 128.18.
I hope this helps!
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Hello!
The formula for the area of a sector can be written as follows:
Area =
(R)
In the above formula, “r” represents the radius while “R” represents the radian measure of a sector. The radius is given to us in the image above as 10 inches. However, we still need the radian measure of the two sectors. To find this measure, we can use the following conversion:
1 degree =
radians
Because the two sectors have a given measure of 72 degrees, we need to multiply both sides of the above conversion by 72:
72 degrees =
Reduce the fraction on the right side of the equation:
72 degrees =
We now have the radian measure of both sectors. Now simply insert this and any other known values into the “area of a sector” formula above:
Area =
()
Simplify the right side of the equation to get the following answer:
Area = 20 pi
We have now proven that the area of one sector is equal to 20 pi.
If, however, you need the combined area of the two identical sectors, simply multiply the proven area by 2 to get a total area of 40 pi.
I hope this helps!
The formula for the area of a sector can be written as follows:
Area =
In the above formula, “r” represents the radius while “R” represents the radian measure of a sector. The radius is given to us in the image above as 10 inches. However, we still need the radian measure of the two sectors. To find this measure, we can use the following conversion:
1 degree =
Because the two sectors have a given measure of 72 degrees, we need to multiply both sides of the above conversion by 72:
72 degrees =
Reduce the fraction on the right side of the equation:
72 degrees =
We now have the radian measure of both sectors. Now simply insert this and any other known values into the “area of a sector” formula above:
Area =
Simplify the right side of the equation to get the following answer:
Area = 20 pi
We have now proven that the area of one sector is equal to 20 pi.
If, however, you need the combined area of the two identical sectors, simply multiply the proven area by 2 to get a total area of 40 pi.
I hope this helps!