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wlad13 [49]
2 years ago
5

A study conducted by the Center for Disease Control that asked 15,000 students about

Mathematics
1 answer:
BaLLatris [955]2 years ago
5 0

Answer:

The sampling distribution of \hat p is: \hat p\sim N(p,\ \frac{p(1-p)}{n}).

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

\mu_{\hat p}=p

The standard deviation of this sampling distribution of sample proportion is:

\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}

The study was conducted using the data from 15,000 students.

Since the sample size is so large, i.e. <em>n</em> = 15000 > 30, the central limit theorem is applicable to approximate the sampling distribution of sample proportions.

So, the sampling distribution of \hat p is: \hat p\sim N(p,\ \frac{p(1-p)}{n}).

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