Imagine that the average weight of a total of 500 girls in a high school is 35kg. Tom randomly sampled 10 girls and measured the
ir weight. And then he repeated this procedure for three times. The means and standard deviations are listed as following. Which sample estimate shows the least sample variability?
1 answer:
Answer:
The sample 2 has a lowest value of SE corresponding to the least sample variability.
Step-by-step explanation:
As the value of the sample means and standard deviations are not given, as similar question is found online from which the values of data is follows
The data is as attached with the solution. From this data
Sample 1 has a mean of 34 and a SE of 5
Sample 2 has a mean of 30 and a SE of 2
Sample 3 has a mean of 26 and a SE of 3
Sample 4 has a mean of 38 and a SE of 5
As per the measure of the sample variability is linked with the value of SE or standard error. Which is lowest in the case of sample 2 .
So the sample 2 has a lowest value of SE corresponding to the least sample variability.
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Let's complete the square
f(x) = x^2 + 6x + 8
y = x^2 + 6x + 8
y-8 = x^2 + 6x
y-8+9 = x^2+6x+9 .... see note below
y+1 = (x+3)^2
y = (x+3)^2-1
note: I added 9 to both sides due to taking half of the 6, and then squaring that result.
We'll restrict x such that to ensure that this function is one-to-one.
Now we need to swap x and y, and solve for y to get the inverse
y = (x+3)^2 - 1
x = (y+3)^2 - 1
x+1 = (y+3)^2
(y+3)^2 = x+1
y+3 = sqrt(x+1)
y = sqrt(x+1)-3
g(x) = sqrt(x+1)-3 is the inverse
The graph is shown below. The original function is in red. The inverse is in blue. The inverse is the result of reflecting the red curve over the dashed line y = x. So this explains why x and y swap places. Consequently, the domain and range also swap as well.
