Testing the Difference between Two Means

High School ・Sociology ・MLA

The first assumption made by the z test is that the populations of the samples used in the study must be distinct. This implies that no other sample population used in the same analysis can be explicitly affected by each sample population used in the study. If the research sample used will impact each other, the study can be biased and lead to incorrect conclusions. To evaluate the degree of association between the variables, a correlation analysis of all sample populations is normally performed.

Secondly, a z test assumes that the populations used to derive sample used in the study have a normal distribution, and the standard deviation of the entire population used in the study must be known and definite (Park). A population is usually normally distributed when items included in the population are large in number. Items in the population should exceed thirty in most cases, for the population to be normally distributed. Failure to use a normally distributed sample results in bias in the study.

The population standard deviation should only be used when the entire population of the study is under analysis. If only a sample of the population is used in the study, then the sample standard deviation should be used in the analysis.

Hypothesis Testing

H0: The difference in monthly social security benefits between disabled workers and retired workers is greater than $30

Step One: Null and Alternative Hypothesis

H1: The difference in monthly social security benefits between disabled workers and retired workers is not greater than $30

Step Two: Collect Data

Data on the monthly social security benefits of two groups is then collected.

Step Three: Calculate the test statistic

The test statistic is then calculated at 0.05 significance level

Step Four: Construct the acceptance and rejection regions for the hypothesis

Using the normal distribution, the acceptance and rejection regions for the analysis is then determined.

Step Five: Drawing conclusion on the null hypothesis

According to the results, the null hypothesis is either accepted or rejected.

Works Cited

Park, HM. Hypothesis testing and statistical power of a test. 2015 https://scholarworks.iu.edu/dspace/bitstream/handle/2022/19738/Hypothesis%20Testing%20and%20Statistical%20Power%20of%20a%20Test.pdf%3Bjsessionid%3DF69B39557BD52F8D2A52951B33ACAFF2?sequence%3D1>.

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