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

H_{0} 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.

H_{1} 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

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 H_{0 }if our p value is less then the significance level

Fail to reject H_{0} if our p value is greater then the significance level

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