STATKEYACT.
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Jan 9, 2024
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MAT 124
Sampling Distribution Activity 3.1
Type in your answers directly on this document. Where directed, copy and paste StatKey graphs into this Word document. Submit this document to Blackboard. Point values are in brackets and this is worth 15 points. Good luck!! 1.
Go to lock5stat.com and open Stat Key. Under sampling distributions select mean. At the top left, under the pinkish stat key button use the dropdown menu to find the data set “Baseball Players -2e (2015 Salary in Millions)”.
a) After selecting this data set at the top right of the screen you can see the population data plotted. For this population:
i. Give the mean using proper population notation and include the unit.
X
̄
= 4.215
[2 pts]
ii. Give the standard deviation using proper population notation. σ = 5.481
[2 pts]
iii. What is the shape of the population distribution? Skewed to the right [2 pts]
b) At the top of the page you should see a default of “select samples of size n = 10”, if it does not say, click into that and change to n=10. Click the button to generate 1000 samples of 10 baseball players from this population. Copy and paste the StatKey graph or sketch it by hand. What is the shape of the dotplot? What does each dot represent? The shape of the dotplot is now symmetrical and each dot represents the salary per 10 players. [4 pts]
c) Now change the sample size to n = 50. Again, generate 1000 samples of 50 baseball players. Now what shape do you see? The dotplot is now bell-shaped. [2 pts]
d) The video mentions if the sample size is sufficiently large then a certain shape will appear for the sampling distribution of the sample mean. The Central Limit Theorem describes this idea. Search online and paraphrase what
the Central Limit Theorem says. [3 pts] The central limit theorem states that the sampling distribution of a sample mean
is approximately normal if
the sample size is large enough, even if the population distribution is not normal.
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