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### How to Calculate the Margin of Error for a Sample Mean

When a research question asks you to find a statistical *sample mean* (or average), you need to report a margin of error, or MOE, for the sample mean. The general formula for the margin of error for the [more…]

### What the Margin of Error Tells You About a Statistical Sample

If you read statistical survey results without knowing the margin of error, or MOE, you are only getting part of the story. Survey results themselves (with no MOE) are only a measure of how the [more…]

### How to Calculate the Margin of Error for a Sample Proportion

When you report the results of a statistical survey, you need to include the margin of error. The general formula for the margin of error for a sample proportion [more…]

### How Sample Size Affects the Margin of Error

In statistics, the two most important ideas regarding sample size and margin of error are, first, sample size and margin of error have an inverse relationship; and second, after a point, increasing the [more…]

### Choosing a Confidence Level for a Population Sample

In statistics, every confidence interval (and every margin of error, for that matter) has a percentage associated with it, called a *confidence level**.* This percentage represents how confident you are that [more…]

### How to Determine the Minimum Size Needed for a Statistical Sample

The margin of error of a confidence interval (CI) is affected by size of the statistical sample; as the size increases, margin of error decreases. Looking at this the other way around, if you want a smaller [more…]

### Creating a Confidence Interval for the Difference of Two Means with Known Standard Deviations

If you know the standard deviations for two population samples, then you can find a confidence interval (CI) for the difference between their means, or averages. The goal of many statistical surveys and [more…]

### How to Create a Confidence Interval for the Difference of Two Means with Unknown Standard Deviations and/or Small Sample Sizes

You can find a confidence interval (CI) for the difference between the means, or averages, of two population samples, even if the population standard deviations are unknown and/or the sample sizes are [more…]

### How to Estimate the Difference between Two Proportions

To estimate the difference between two population proportions with a confidence interval, you can use the Central Limit Theorem when the sample sizes are large enough [more…]

### How to Find the Cutoff Point for Rejecting a Null Hypothesis

In statistics, if you want to draw conclusions about a null hypothesis H_{0} (reject or fail to reject) based on a *p-*value, you need to set a predetermined cutoff point where only those [more…]

### How to Calculate a Confidence Interval for a Population Mean When You Know Its Standard Deviation

If you know the standard deviation for a population, then you can calculate a confidence interval (CI) for the mean, or average, of that population. When a statistical characteristic that’s being measured [more…]

### Why Margin of Error and Confidence Intervals Matter in Statistics

Statistical results should always include a margin of error and confidence intervals. This information is important because you often see statistics that try to estimate numbers pertaining to an entire [more…]

### How to Calculate a Confidence Interval for a Population Mean with Unknown Standard Deviation and/or Small Sample Size

You can calculate a confidence interval (CI) for the mean, or average, of a population even if the standard deviation is unknown or the sample size is small. When a statistical characteristic that’s being [more…]

### How to Determine the Confidence Interval for a Population Proportion

You can find the confidence interval (CI) for a population proportion to show the statistical probability that a characteristic is likely to occur within the population. [more…]

### How to Set Up a Hypothesis Test: Null versus Alternative

When you set up a hypothesis test to determine the validity of a statistical claim, you need to define both a null hypothesis and an alternative hypothesis. [more…]

### How to Determine a *p*-Value When Testing a Null Hypothesis

When you test a hypothesis about a population, you can use your test statistic to decide whether to reject the null hypothesis, H_{0}. You make this decision by coming up with a number, called a [more…]