A pharmaceutical company searching for a new antibiotic is investigating the effect of 2000 different compounds on a disease causing bacteria. For each compound they perform an experiment and evaluate the experiment at a significance level of α = 0.05. If none of the compounds have any effect on the bacteria, how many of the experiments do we expect to produce a statistically significant result (i.e. we reject H0)
The hypothesis being tested are,
Ho: The compound has no significant effect on the bacteria.
H1: The compound has a significant effect on the bacteria.
Now, we know that none of these compounds are effective, which means we must accept Ho for all the 2000 compounds.
But, level of significance = 0.05 i.e the probability of committing Type I error.
Type I error is to Reject Ho when it is true.
This means that even if we know that Ho is true, the test tends to make an error of rejecting Ho 5% of the time.
Thus, for 5% of 2000 compounds we will conclude that it is significant even if it's not which is equal to 2000×0.05 = 100
So, for 100 compounds, we are expected to conclude that the result was statistically significant
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