Walter and Trina are planning a campus event focused on equity and inclusion. Several students would like to help with the event
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Sampling distribution involves the proportions of a data element in a given sample.
- <em>The proportion of Good TV set is 0.67</em>
- <em>The number of ways of selecting 5 from 6 TV sets is 6</em>
- <em>The number of ways of selecting 4 from 6 TV sets is 15</em>
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Given
Sample Space = Good, Good, Defective, Defective, Good, Good
<u>(a) Proportion that are good</u>
From the sample space, we have:
So, the proportion (p) that are good are:
<u>(b) Ways to select 5 samples (without replacement)</u>
This is calculated using:
Where
So, we have:
Hence, there are 6 ways
<u>(c) All possible sample space of 4</u>
First, we calculate the number of ways to select 4.
This is calculated using:
Where
So, we have:
So, the table is as follows:
The proportion column is calculated by dividing the number of Good TVs by the total selected (4) i.e.
<u>(d) The sampling distribution</u>
In (a), we have:
--- proportion of Good TV
The sampling error is calculated as follows:
So, we have:
Read more about sampling distributions at: