Sampling variation, standard errors and model conditions.
Example 1
In a random sample of 500 voters, 200 support a proposal. Find the sample proportion.
Show worked answer
Answer: 0.4
- Sample proportion =sample sizesupporters=500200=0.4.
Example 2
The population proportion is 0.2. For independent samples of 200, find the standard deviation of the sample proportion. Give your answer to 4 decimal places.
Show worked answer
Answer: 0.0283
- SD(p^)=√np(1−p).
- Substitute √0.2×2000.8.
- Rounded answer: 0.0283.
Example 3
For n=50 and p=0.4, a normal approximation to the sample proportion is considered. Using the rule np ≥10 and n(1−p)≥10, are both count conditions met?
Show worked answer
Answer: Yes: both expected counts are at least 10
- np=20; n(1−p)=30.
- Yes: both expected counts are at least 10. Independence and random sampling are also needed.