Vivian Abadi
06/13/24
ENV 1004
HW #4
7. Reset the fish sampling visualizer by clicking on "Return to start" located at the bottom of the
simulator. Enter the following model parameters:
N = 100
μ = 100
σ = 20
Go ahead and make a “complete sample of 100” and “show sampling distribution” to see the
smoothed distribution line. Now, click on μ and drag it back and forth.
a. Does the position of the distribution change?
Yes- moves right if going up in numbers and left if going down
b. What about the shape of the distribution? Briefly describe what’s going on here.
No the shape does not change. We are simply changing the average fish length but that
does not affect the deviation directly.
8. Set the same starting values as question 1. Now click on σ and drag it back and forth, ranging
from 5 to 40. Watch what happens to the distribution.
a. Does the position of the distribution change? No
b. What about the shape of the distribution? Briefly describe what’s going on here.
The shape of the distribution gets wider as σ gets larger and narrower as it gets smaller.
This is because a larger σ means more variation.
11. Now try using 99% confidence intervals. What happens to the ranges when you switch to
99% confidence intervals? Do they get larger or smaller? Why?
They get larger- this is because when there are longer intervals, it is much more likely that the
mean is included in the interval.
12. Increase the sample size by dragging the “n 10” button to the right. Were the confidence
intervals wider or narrower with n= 40 than when n= 10? Why do you think that is?
06/13/24
ENV 1004
HW #4
7. Reset the fish sampling visualizer by clicking on "Return to start" located at the bottom of the
simulator. Enter the following model parameters:
N = 100
μ = 100
σ = 20
Go ahead and make a “complete sample of 100” and “show sampling distribution” to see the
smoothed distribution line. Now, click on μ and drag it back and forth.
a. Does the position of the distribution change?
Yes- moves right if going up in numbers and left if going down
b. What about the shape of the distribution? Briefly describe what’s going on here.
No the shape does not change. We are simply changing the average fish length but that
does not affect the deviation directly.
8. Set the same starting values as question 1. Now click on σ and drag it back and forth, ranging
from 5 to 40. Watch what happens to the distribution.
a. Does the position of the distribution change? No
b. What about the shape of the distribution? Briefly describe what’s going on here.
The shape of the distribution gets wider as σ gets larger and narrower as it gets smaller.
This is because a larger σ means more variation.
11. Now try using 99% confidence intervals. What happens to the ranges when you switch to
99% confidence intervals? Do they get larger or smaller? Why?
They get larger- this is because when there are longer intervals, it is much more likely that the
mean is included in the interval.
12. Increase the sample size by dragging the “n 10” button to the right. Were the confidence
intervals wider or narrower with n= 40 than when n= 10? Why do you think that is?
