Describe to your classmates the difference between confidence interval for μ1−μ2 and for the hypothesis test for μ1−μ2. How would you explain the differences?
Describe to your classmates the difference between confidence interval for μ1−μ2
Firstly, describe to your classmates the difference between confidence interval for μ1−μ2 and for the hypothesis test for μ1−μ2. How would you explain the differences?
More details;
Comparing Two Population Means
In this section, we are going to approach constructing the confidence interval and developing the hypothesis test similarly to how we approached those of the difference in two proportions.
There are a few extra steps we need to take, however. First, we need to consider whether the two populations are independent. When considering the sample mean, there were two parameters we had to consider. <span id="MathJax-Element-1-Frame" class="mjx-chtml MathJax_CHTML" style="-webkit-font-smoothing: antialiased; text-shadow: none !important; box-shadow: none !important; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 19.2px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="μ”>μ the population mean, and also <span id="MathJax-Element-2-Frame" class="mjx-chtml MathJax_CHTML" style="-webkit-font-smoothing: antialiased; text-shadow: none !important; box-shadow: none !important; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 19.2px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="σ”>σ the population standard deviation. The second step is to determine if we are in a situation where the population standard deviations are the same. Or if they are different.
Independent and Dependent Samples
It is important to be able to distinguish between an independent sample or a dependent sample.
- Independent sample
- The samples from two populations are independent if the samples selected from one of the populations. It has no relationship with the samples selected from the other population.
- Dependent sample
- The samples are dependent (also called paired data) if each measurement in one sample is matched. Or paired with a particular measurement in the other sample. Another way to consider this is how many measurements are taken off of each subject. If only one measurement, then independent. If two measurements, then paired. Exceptions are in familial situations such as in a study of spouses or twins. In such cases, the data is almost always treated as paired data.
The following are examples to illustrate the two types of samples.