Paired T Test


What if we want to determine whether a restaurant time for food to come out is faster when there is a manager present to when there is no manager present. For this we would need a paired t test.

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 mean time for our meal to come out is 25 minutes regardless of whether there is a manager or no manager.
  • H1 is our alternative hypothesis and assumes that the differences between what we observed and what we expected is of statistical significance.
    • The mean time for our meal to come out differs when there is a manager as opposed to no manager.

Step 2: Analyze evidence


  • 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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