# Confidence interval margin of error relationship goals

### Confidence Intervals Definitions. Relationships. Calculations. Margin of. Error. Summary. Power and Sample Size Calculations depends on. Scientific goals . confidence interval will not be so wide as to include both clinically significant. Although we work with samples, our goal is to describe and draw inferences This range is the confidence interval (CI) which is estimated on the basis of general form: CI = Point estimate ± Margin of error, where the margin of error of P only suggests whether there is any difference in probability terms. One can compute confidence intervals all types of estimates, but this short module will The goal of exploratory or descriptive studies is not to formally compare groups . The margin of error is very small here because of the large sample size.

Confidence intervals for means Video transcript - [Instructor] We're told Della wants to make a one-sample z interval to estimate what proportion of her community members favor a tax increase for more local school funding.

### Margin of error - Wikipedia

What is the smallest sample size required to obtain the desired margin of error? So let's just remind ourselves what the confidence interval will look like and what part of it is the margin of error, and then we can think about what is her sample size that she would need.

So she wants to estimate the true population proportion that favor a tax increase. She doesn't know what this is, so she's going to take a sample size of size n, and in fact this question is all about what n does she need in order to have the desired margin of error. Well whatever sample she takes there, she's going to calculate a sample proportion.

And then the confidence interval that she's going to construct is going to be that sample proportion plus or minus critical value, and this critical value is based on the confidence level.

We'll talk about that in a second. And so in this case it would be the square root, it would be the standard error of her sample proportion, which is the sample proportion times one minus the sample proportion, all of that over her sample size. So the margin of error is this part right over here. It's unpleasant, all right. So how do we figure that out?

## Introduction

So we could look at a z-table. So this would be 2. You would look up the percentage that would leave 2. So you would actually look up And that's just something good to know. We could of course look it up on a z-table. So this is 1. And so this is going to be 1. But what about p hat? We don't know what p hat is until we actually take the sample, but this whole question is, how large of a sample should we take.

## Margin of error

However,we will first check whether the assumption of equality of population variances is reasonable. The ratio of the sample variances is 9.

The solution is shown below. First, we compute Sp, the pooled estimate of the common standard deviation: Note that again the pooled estimate of the common standard deviation, Sp, falls in between the standard deviations in the comparison groups i.

### Determining sample size based on confidence and margin of error (video) | Khan Academy

Our best estimate of the difference, the point estimate, is The standard error of the difference is 6. In this sample, the men have lower mean systolic blood pressures than women by 9. Again, the confidence interval is a range of likely values for the difference in means. Since the interval contains zero no differencewe do not have sufficient evidence to conclude that there is a difference. Confidence Intervals for Matched Samples, Continuous Outcome The previous section dealt with confidence intervals for the difference in means between two independent groups. There is an alternative study design in which two comparison groups are dependent, matched or paired.

How do I interpret and calculate a confidence interval for an estimate in a single sample? After successfully completing this unit, the student will be able to: Explain what a confidence interval is. Interpret the confidence interval for a mean or a proportion from a single group. Use R to compute a confidence interval for the mean in a single group Use R to compute a confidence interval for a proportion in a single group Estimating Population Parameters in a Single Group The goal of exploratory or descriptive studies is not to formally compare groups in order to test for associations between exposures and health outcomes, but to estimate and summarize the characteristics of a particular population of interest. Typical examples would be a case series of humans who had been diagnosed and treated for bird flu or a cross-sectional study in a community for the purpose of better understanding the current health status and potential challenges for the future.

The variables being estimated would logically include both continuous variables e. For both continuous variables e.