# Paired T-test Bug example

A farmer has one paddock which is infested with bugs, he wants to determine whether his insecticide is effective at treating and killing the bugs. In order for his experiment to be valid he has to compare the number of bugs before treatment to the number of bugs after treatment. He randomly samples different plants in the paddock, counting how many bugs he sees on each plant he samples. He then repeats the same process for the same plants after he treats the paddock.

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Step 1: Hypothesis

• H0 is our null hypothesis i.e. the difference between what we observe and what we expected to observe is null and is a result of normal fluctuations.
• The number of bugs before and after treatment is no different
• H1 is our alternative hypothesis and assumes that the differences between what we observed and what we expected is of statistical significance.
• There is a difference in the number of bugs before and after treatment.

Step 2: Analyze evidence

Assumptions

• All data is independent: i.e. we measure the time for multiple meals to come out at different tables throughout the night – we are not just measuring the time for one table’s meals to come out throughout the night.
• The population follows a normal distribution: i.e. the times of different tables can be plotted and follow a normal distribution

Find your test statistic and p value

Step 3: Draw a conclussion

• So reject H0 if our p value is less then the significance level
• Fail to reject H0 if our p value is greater then the significance level

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