ECON 1011 Lecture Notes - Lecture 11: Null Hypothesis, Confidence Interval, Statistical Hypothesis Testing
16 May 2018
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More about Tests and Intervals
Chapter 12
Alpha Levels and Significance
In the last few lectures we learnt how to calculate the p-value for our test statistics.
The p-value tells us what the probability of observing the statistic (e.g. sample proportion, mean) if the null
hypothesis is true.
When the p-value is low (high), the data we observe would be unlikely (likely) if null hypothesis is true.
Accordingly we reject (fail to reject) the null. But how low is low enough?
We can define this by setting a threshold for our p-value such that if the p-value falls below the threshold, we
will reject the null hypothesis.
This threshold is alled a alpha leel α, or significance level.
If the p-value for a hypothesis test falls below alpha level, we refer to the test as being statistically significant.
Common alpha levels are 0.10, 0.05, 0.01, 0.001.
Confidence Intervals and Hypothesis Test
Confidence intervals and hypothesis tests are built from the same calculations.
One can approximate a hypothesis test by examining the confidence interval.
Given that confidence intervals are two-sided, they correspond to two sided hypothesis tests.
Example:
Going back to the example of the new manager of a small convenience store who randomly sampled 20
purhases fro yesterday’s sales.
Suppose that the 95% confidence interval is (35.59, 54.93), is there evidence that the mean purchase amount
is different from $40?
The 95% confidence interval contains $40 as a plausible value.
At alpha level = 0.05, we would fail to reject the null that the mean purchase is different from $40.
find more resources at oneclass.com
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Document Summary
In the last few lectures we learnt how to calculate the p-value for our test statistics. The p-value tells us what the probability of observing the statistic (e. g. sample proportion, mean) if the null hypothesis is true. When the p-value is low (high), the data we observe would be unlikely (likely) if null hypothesis is true. Accordingly we reject (fail to reject) the null. We can define this by setting a threshold for our p-value such that if the p-value falls below the threshold, we will reject the null hypothesis. This threshold is (cid:272)alled a(cid:374) alpha le(cid:448)el (cid:894) (cid:895), or significance level. If the p-value for a hypothesis test falls below alpha level, we refer to the test as being statistically significant. Common alpha levels are 0. 10, 0. 05, 0. 01, 0. 001. Confidence intervals and hypothesis tests are built from the same calculations. One can approximate a hypothesis test by examining the confidence interval.
