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This year he checks a small sample of apples and the sample average x is 18 kg.ĭid the average weight of apples change over the past year? The statistical decision will be based on the difference between the know Mean and the sampleĮxample: A farmer calculated last year the average weight of apples in his orchard (μ0) is 17 kg, based on a big sample. The null hypothesis assumes that the known mean is correct.
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We use this test to check if the known Mean is statistically correct, based on a sample average and sample standard deviation. The higher the degree of freedom the more it resembles the normal distribution. The shape depends on the degrees of freedom which is usually the number of independent observations minus one (n-1). This makes it more realistic than Normal distribution, as for small size the average and standard deviation estimation are less accurate T distribution looks similar to the normal distribution but lower in the middle and with thicker tails. Student's T distribution is an artificial distribution used for a normally distributed population when we don't know the population's standard deviation.
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When the sample is more than 30 you should still use the T Distribution, but using the normal distribution instead will support similar results. We usually use the T-test(s) to compare the sample average (Mean) to the known mean or to compare between the averages of two groups, when we don’t know the standard deviation The t-test is not one test, but a group of tests which constitutes of all statistical tests which distribute as T Distribution (Student’s).