Step 4: Using the z-table, determine the rejection regions for you z-test. So, the z-test result, also called the test statistic is 62.5. This Site has several examples under the Stats Apps link. However, there are many applications that run such tests. In this example, we are using the z-test and are doing this by hand. NOTICE2: The Ho is the null hypothesis and so always contains the equal sign as it is the case for which there is no significant difference between the two groups. In a two-tailed test, the Ha contains a NOT EQUAL and the test will see if there is a significant difference (greater or smaller). NOTICE1: The Ha in this example is ONE-TAILED because we are interested in seeing if New Jersey is significantly GREATER than the population mean. Ha: mean per student per year funding for New Jersey > mean per student per year funding for the USA Ho: New Jersey mean – Population mean = 0 This can also be written as the following. Ho: mean per student per year funding for New Jersey = mean per student per year funding for the USA NOTE: There are many ways to write out Ho. Hypothesis: The mean per student per year funding in New Jersey is significantly greater than the average per student per year funding over the entire USA. If you do not have this information, it is sometimes best to use the t-test. To run a z-test, it is generally expected that you have a larger sample size (30 or more) and that you have information about the population mean and standard deviation. Using the dataset, you would need to first calculate the sample mean.
NOTE: This entire example works the same way if you have a dataset. Use the z-test and the correct Ho and Ha to run a hypothesis test to determine if New Jersey receives significantly more funding for public school education (per student per year). Next, suppose you collect a sample (n = 100) and determine that the sample mean for New Jersey (per student per year) is $8801. You know that the USA mean public school yearly funding is $6300 per student per year, with a standard deviation of $400. Suppose it is up to you to determine if a certain state receives significantly more public school funding (per student) than the USA average.
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