This is one question for statistics that I\'ve split into five different parts t

Question

This is one question for statistics that I've split into five different parts to make it more organized.

What is the formula for standard error of a distribution for a difference in two sample proportions (i.e., sampling distribution of difference in proportions)?

What is the z-score formula for a hypothesis test for difference in proportions?

The standard normal distribution can be used to compute a p-value for a hypothesis test of the difference in two proportions if the sample sizes are “sufficiently large.” What rule does the book use to decide if the sample sizes are sufficiently large to conduct a hypothesis test of the difference in two proportions?

What is the formula for standard error of a distribution for a difference in two sample means (i.e., sampling distribution of difference in means)?

“For small sample sizes (n1 < 30 or n2 < 30), the t-distribution is only a good approximation if the

underlying population has a distribution that is approximately ________________.” Fill in the blank with one word.

Explanation / Answer

For the difference in proportions:

When p1 and p2 are the proportions and n1 and n2 are sample sizes. Let 1 and 2 be the standard deviations.

Standard Error:

SEp1 - p2 = sqrt{ [p1 * (1 - p1) / n1] + [p2 * (1 - p2) / n2] }

Z-Score:

Z= (p1p2)/sqrt{p(1p)(1/n1+1/n2)}

The rule is both n1 and n2 > 30

For the difference in means:

Let x1 and x2 be the sample means that we have; n1 and n2 be sample sizes. 1 and 2 be the standard deviations.

Standard Error :

sqrt(1^2/n1 + 2^2/n2)

The blank is- Normal

Hope this helps and Please don't forget to rate the answer :)

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