Activity 1: Making estimates from samples

Teacher notes here

"I wonder what the median weight of New Zealand Kiwi is?"

Take 5 samples, and use them to answer your investigative question

Instructions (also on student Google Doc)

Use this link to take a sample of n=15 kiwis. Leave the “select variable” blank
Take your sample into iNZight lite by scrolling to the bottom of the page and selecting the “iNZight Lite” button
Create a dot plot/box plot of your sample of 15 kiwis by changing the “Select first variable:” option to “Weight.kg.”
Snip your plot into the SAMPLE 1 section in the table on page 2 of the Google Doc
Click the “summary statistics” tab and find the median
Write the median for Sample 1 in the table on page 2 of the Google Doc
REPEAT! four times to completely fill in the table
Use your samples to answer your investigative question (head to the CONCLUSION section after your table)

Make copies of the necessary documents by clicking below....

Student Document

Class spreadsheet

Slideshow to assist with running the activity....

Slideshow

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Understanding Sampling variation

The variation in a sample statistic from sample to sample.

Suppose a sample is taken and a sample statistic, such as a sample median, is calculated. If a second sample of the same size is taken from the same population, it is almost certain that the sample median calculated from this sample will be different from that calculated from the first sample. If further sample medians are calculated, by repeatedly taking samples of the same size from the same population, then the differences in these sample medians illustrate sampling variation.

Sampling variation animations - https://www.stat.auckland.ac.nz/~wild/WPRH/

Understanding Sampling error

The error that arises in a data collection process as a result of taking a sample from a population rather than using the whole population.

Estimates from different random samples (of the same size) will vary from sample to sample, and each estimate is likely to be different from the true value of the population parameter.

The sampling error for a given sample is unknown but when the sampling is random, for some estimates (for example, sample mean, sample proportion) theoretical methods may be used to measure the extent of the variation caused by sampling error.

The need for a 'Confidence Interval'

In a real world situation we would only take one sample. Given our understanding of sampling error, we know the sample median from this single sample will only be an estimate of the population median.

We would suggest that the population median is somewhere around the sample median we have found. A nice way to present this is in the form of an interval, so we could say that we think the population median is somewhere between here and here. So we want to add a little bit on and take a little bit off our sample median to create an interval.......but how much should we add on /take off??

This will all depend on how much Sampling error is present in the situation. More sampling error would mean we need a wider interval to be confident it captures the true population median. Less sampling error would mean we can have a narrower interval. (We also don't want to just make the interval extremely wide so that we know it contains the true population median, the wider the interval becomes the less useful it becomes.)

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