## What is sampling distribution of sample proportion?

The Sampling Distribution of the Sample Proportion If repeated random samples of a given size n are taken from a population of values for a categorical variable, where the proportion in the category of interest is p, then the mean of all sample proportions (p-hat) is the population proportion (p).

**What is the relationship between the center of the distribution of the sample proportions and the value of the population proportion?**

IV. Ask students to speculate about the relationship between the center of the distribution of the sample proportions and the value of the population proportion. Students should note that the distribution of sample proportion values is centered on the value of the population proportion (1/6 is approximately . 17).

**What is the probability that the random sample of 1500 students will give a result within 2 percentage points of this true value?**

About 90%

About 90% of all SRSs of size 1500 will give results within 2 percentage points of the truth about the population.

### What is the formula for sampling distribution?

The formula is μM = μ, where μM is the mean of the sampling distribution of the mean.

**How do you find the sampling distribution of proportions?**

The Sampling Distribution of the Sample Proportion. For large samples, the sample proportion is approximately normally distributed, with mean μˆP=p. and standard deviation σˆP=√pqn. A sample is large if the interval [p−3σˆp,p+3σˆp] lies wholly within the interval [0,1].

**What is the sampling distribution model for a difference between proportions?**

A normal model is a good fit for the sampling distribution of differences if a normal model is a good fit for both of the individual sampling distributions. More specifically, we use a normal model for the sampling distribution of differences in proportions if the following conditions are met.

#### What is the difference between the sampling distribution of a proportion and the sampling distribution of a mean?

The mean of each sampling distribution of individual proportions is the population proportion, so the mean of the sampling distribution of differences is the difference in population proportions.

**What is the probability that a SRS of size 125 will give a result within 7 percentage points of the true value?**

About 95%

Answer: About 95% of all SRSs of size 125 will give a sample proportion within 7 percentage points of the true proportion of middle school students who are planning to attend a four-year college or university.

**What is the probability that the sample proportion will be within 2 percentage points of the population proportion?**

We see that almost 90% of all samples will give a result within 2 per- centage points of the truth about the population.

## How do you find the sample size for a sampling distribution?

For samples of any size drawn from a normally distributed population, the sample mean is normally distributed, with mean μX=μ and standard deviation σX=σ/√n, where n is the sample size.

**How do you calculate distribution?**

Add the squared deviations and divide by (n – 1), the number of values in the set minus one. In the example, this is (1 + 4 + 0 + 4 + 4) / (5 – 1) = (14 / 4) = 3.25. To find the standard deviation, take the square root of this value, which equals 1.8. This is the standard deviation of the sampling distribution.