The following are some recommended practical self-assessment questions for the lesson called Introduction to Hypothesis Testing by Example for Geospatial Contexts. They’re intended for you to work through to test your own ability to apply the key concepts we covered there.
Note: You may need to use Excel’s NORMSINV() and TINV() functions for these problems in cases not represented in the printed tables.
a) Repeat Hypothesis Testing Steps 4, 5, and 6 of Example 1 from the notes using a level of statistical significance of 31.74% (i.e. akin to a level of confidence of 68.26%). This is an unusually high value for a hypothesis test, but I want you to do it and think it through.
b) You should have gone from failing to reject in the original Example 1 to rejecting in a). Can you explain why this is? Does this help you see / explain why the standard error isn’t enough when looking at the precision of our estimated parameters?
In Example 2 from the notes, how big would the standard deviation of the error in the measurements need to have been for us to have failed to reject m? Can you interpret this result? What’s the deal?
Imagine that the true distance from A to B wasn’t known and repeat the original Example 2. Do and show the results from all six steps.
Okay, so we’ve beaten the question of the 5th measurement in Example 2 to death. Now let’s move ahead assuming that it is indeed a gross error.
If you just throw out the 5th measurement (since you have five other measurements of the same distance available):
a) What would be your best estimate of the distance and its precision? With regard to precision, be sure to make a statement expressing what it is you are confident about, as we did when we studied confidence intervals.
Use a 1% statistical significance for this (which is akin to a 99% confidence level), and continue to assume that is known to be 4.0 cm and that the errors in the measurements are normally distributed and not correlated to each other.
b) Now imagine that someone has suggested that the actual distance between points A and B has changed because the monument at point A on the ground has moved. Set up and carry out a hypothesis test of the claim that the true distance is now different from 500.0 m. Follow and share the results from all six hypothesis testing steps.
Use the same statistical significance and assumptions about .
c) For a two-tailed test like this, could you have known from the confidence interval – i.e. before doing part b) – whether or not your test in b) was going to reject ? How so?
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