Consider making inferences about p1 and p2 Please copy link http://imgur.com/a/b

Question

Consider making inferences about p1 and p2

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http://imgur.com/a/bhmI1

The dropdown menue is Possion, binomial, normal.

Consider making an inference about p_1 - p_2, where there are x_1 successes in n_1 binomial trails and x_2 successes in n_2 binomial trails. a. Describe the distributions of x_1 and x_2. b. Explain why the Central Limit Theorem is important in finding an approximate distribution for (p_1 - p_2). a. Choose the correct distributions below. x_1 has a distribution and x_2 has a distribution. b. Choose the correct explanation below. A. The sampling distribution of (p_1 - p_2) remains the same for large samples. B. The sampling distribution of (p_1 - p_2) is skewed for large samples. C. The sampling distribution of (p_1 - p_2) is approximately normal for large samples.

Explanation / Answer

a.

The number of successes X in n trials of a binomial experiment is called a binomial random variable. The probability distribution of the random variable X is called a binomial distribution.

So, x1 has a binomial distribution and x2 has a binomial distribution.

b.

By central limit theorem, the sampling distribution of difference in proportions is approximately normally distributed if N is fairly large.
So, the correct option is,
C. The sampling distribution of (p1 - p2) is approximately normal for large samples.

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