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Sagot :
Answer:
The standard deviation of the distribution of sample proportions is 0.0229.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
70% of all city residents support the tax increase to build a combined bus and train station.
This means that [tex]p = 0.7[/tex]
400 city residents
This means that [tex]n = 400[/tex]
What is the standard deviation of the distribution of sample proportions?
By the Central Limit Theorem:
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.7*0.3}{400}} = 0.0229[/tex]
The standard deviation of the distribution of sample proportions is 0.0229.
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