# Z test

A z test can be used when our data follows a normal distribution. This test looks at the mean of the distribution.

We can use this test if we want to determine the mean time for your meal to come out at the restaurant with 5 staff on. Our research question is: Is the mean time for our meal to come out at a restaurant 25 minutes?

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
• 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 is not 25 minutes

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
• We have to know the standard deviation of all times throughout the night

Test statistic = the (observed value – expected value) / standard error

The largest the test statistic, the larger the difference between the observed and expected value hence more evidence that you should reject H0

However, you have to use the P-test to determine whether your test statistic is over any significance.

• 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

Step 3: Conclusion

Therefore, you can chose to accept or fail to reject H0.

Note: you can never prove anything you just fail to reject it.

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