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Two-tailed hypothesis tests and analyze t-test and z-test
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•(1) Explain when to use a t-test and when to use a z-test. Explore the differences.                                                                                    
•(2) Discuss why samples are used instead of populations.                                                                                        
                                                                                                     
                                                                                                     
(1)                                                                                                    
The z- test and t- test are basically the same; they compare two means to suggest whether the two samples come from the same population.  These tests can also be used to examine whether the mean has a specified value. There are variations in the t- test. If you have a sample and wish to compare it with a known mean the single sample t- test is available. If your samples are not independent of each other and have some factor in common, i.e. geographical location or before/after treatment, the paired sample t- test can be applied. There are also two variations on the two sample t- test, the first uses samples that do not have equal variances and the second uses samples whose variances are equal.
A z- test is applicable if the data satisfies the following conditions:                                                                                        
(a) The data points should be independent of each other                                                                                           
(b) The sample size, n > 30                                                                                                
(c) If n < 30, the distribution should be normal. (If n > 30 the distribution of the data does not matter)                                                                                  
(d) Random sampling                                                                                                 
A t- test is applicable if the data satisfies the following conditions:                                                                                        
(a) The data sets should be independent from each other except in the case of the paired-sample t- test                                                                                 
(b) If n < 30 the use of t- test is mandatory                                                                                             
(c) The distributions should be normal for the equal and unequal variance t-test                                                                                       
(d) Random sampling                                                                                                
                                                                                                     
                                                                                                     
(2)                                                                                                    
A sample is a subset of population.  The set of individuals, items, or data from which a statistical sample is taken is population. A population is any collection of people, animals, plants or things from which we may collect data. It is the entire group we are interested in, which we wish to describe or draw conclusions about. A sample is a group of units selected from a larger group (the population). By studying the sample we hope to draw valid conclusions about the population.          
It is impossible to study an entire population. Based on the analysis of a small sample we infer about population parameters and take an appropriate decision regarding the population. A scientifically selected sample reduces the cost of the entire analysis and saves time without compromising on the accuracy of the estimates.                                      
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
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