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Sagot :
Answer:
For this sample, the estimated standard error is of 0.0277
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]
Examining the records of 250 convicts, the official determines that there are 65 cases of recidivism.
This means that [tex]n = 250, p = \frac{65}{250} = 0.26[/tex]
For this sample, the estimated standard error is
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.26*0.74}{250}} = 0.0277[/tex]
For this sample, the estimated standard error is of 0.0277
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