Hypothesis Testing: Critical values & Rejection Regions I Statistics 101 #4 | MarinStatsLectures

Hypothesis Testing: Critical values & Rejection Regions I Statistics 101 #4 | MarinStatsLectures


Significance levels and critical values
help us decide whether or not we should reject our null hypothesis. Recall we are
using the following null and alternative hypotheses and we have found that Kian’s
average IQ score of 117 is 13 points below 130 and in terms of a test
statistic it is 2.6 standard errors below 130. we’ve already noted that we
must ask the question how far must the average drop below 130 before we are
willing to reject our null? this is the idea behind a critical value:
we must select the false rejection rate we call this the significance level. 5% is the most commonly used significance level so let’s use that!
assuming the null hypothesis is true and the standard error of 5, the sampling
distribution of the average would look as follows: using the standard normal
distribution as an approximation, roughly 5% of values fall more than
1.65 standard errors below the mean. Converting this back to IQ score
approximately 5% of averages will fall below 121.75; in other words
if his IQ really is 130 approximately 5% of the time we’d end up
with an average IQ score of 121.75 or less by chance or a test statistic of
-1.65 or less by chance! we call the IQ of 1201.75 or the test
statistic value of -1.65 the critical values and the area below them
the rejection region. For values below those we will reject our null hypothesis.
In our example the sample average is 117 and the test statistic is -2.6 and these fall below the critical values into the rejection region and so
we will reject the null hypothesis. If we want to be less likely to falsely reject the null we would use a smaller value for the significance level and hence a
cut-off that is further from the Null. thanks for watching this video, don’t
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