## 3.6 Activity: Introduction to estimation: Monday Breakups

In a previous course activity, we found that breakups are more likely to happen on Mondays. But just how likely are Monday breakups? In this activity, you will address the following question,

What proportion of breakups are reported on Mondays?

The evidence we have comes from a sample. In a random sample of 50 breakups on Facebook, 26% were reported on Monday. The research question, though, is about all breakups reported on Facebook, not just the breakups in the sample. Thus, we are interested in estimating a population parameter (the proportion of all breakups reported to Facebook) based on a sample.

Sample: Random sample of 50 breakups reported to facebook.

Population: All breakups reported to facebook

In this activity we’ll explore how statisticians go about estimating a population parameter using data from a sample.

### 3.6.1 Estimation intuitions

What is the best estimate for the population paramater? What other estimates are compatible with our sample?

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3.6.1: Monday breakups: Estimation intuitions
##### Vocab
• We use the term population parameter to refer to the value that we want to estimate in the population. For example, the proportion of all breakups on facebook that are reported on Monday.
• We use the term sample statistic to refer to observed result in the sample. For example, the proportion of Monday breakups in the random sample.

### 3.6.2 Estimating samping variabilty

In the first part of the activity, we explored how researchers can make a statistical estimate about a population parameter from a representative sample.

The key points so far are:

1. The sample statistic (the observed result) is the best estimate of the population parameter
2. There is some uncertainty in the estimate due to sampling variation.
3. Just because there is uncertainty does not mean that anything goes. Some estimates for the population parameter are compatible with the sample and other estimates are not compatible with the sample.

If we apply these key points to our study, we can say:

We estimate that approximately 26% of all breakups on Facebook are reported on Monday. However, there is some uncertainly in this estimate due to sampling variation.

Because of sampling variation, when answering research questions that ask for an estimate, it is important that we acknowledge that there is uncertainty in the estimate.

At the same time, there is regularity in randomness. Even though there is sampling variability, it is not the case that anything goes.

So just how much uncertainty is there? Remember, the uncertainty comes from sampling variation. If we could measure the expected sampling variation, we could quantify the uncertainty in our estimate.

If we had access to the entire population, we could estimate sampling variability using Monte Carlo simulation. We would put the entire population into a mixer and then repeatedly draw random samples of size n=50 from the population. We would collect the proportion of Monday breakups in each simulated sample. Across multiple trials a pattern would emerge, and we could use the resulting sampling distribution to estimate the sampling variability.

The problem is, we don’t have access to the entire population. We only have one sample of size n=50. In this activity, you will explore the question,

How can we estimate sampling variabiltiy when we only have one sample?

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3.6.2: Monday breakups: Estimating sampling variability
3.6.3: Monday breakups: Quantifying uncertainty