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the program is not effectiveįrom the box plot in Figure 2 we see that the data is quite symmetric and so we use the t-test even though the sample is small.Ĭolumn E of Figure 1 contains all the formulas required to carry out the t test. from an earlier study, that overall weight gain is unlikely). Usually, we conduct a two-tailed test since there is a risk that the program might actual result in weight gain rather than loss, but for this example, we will conduct a one-tailed test (perhaps because we have evidence, e.g. We judge the program to be effective if there is some weight loss at the 95% significance level. Can we conclude that the program is effective?Ī negative value in column B indicates that the subject gained weight. To test this claim 12 people were put on the program and the number of pounds of weight gain/loss was recorded for each person after two years, as shown in columns A and B of Figure 1. The coefficient of skewness is relatively smallĮxample 1: A weight reduction program claims to be effective in treating obesity.The mean is approximately equal to the median.the median is in the center of the box and the whiskers extend equally in each direction The boxplot is relatively symmetrical i.e.The following are indications of symmetry: This can be determined by graphing the data. It turns out that the t distribution provides good results even when the population is not normal and even when the sample is small, provided the sample data is reasonably symmetrically distributed about the sample mean.
#ONE SAMPLE T HYPOTHESIS TEST CALCULATOR HOW TO#
Together we will work through various examples of how to create a hypothesis test about population means using normal distributions and t-distributions.The t distribution provides a good way to perform one-sample tests on the mean when the population variance is not known provided the population is normal or the sample is sufficiently large so that the Central Limit Theorem applies (see Theorem 1 and Corollary 1 of Basic Concepts of t Distribution). And if our sample size is less than 30, we apply the Central Limit Theorem and deem our distribution approximately normal. And as we learned while conducting confidence intervals, if our sample size is larger than 30, then our distribution is normal or approximately normal. If the population standard deviation is known, then our significance test will follow a z-value. How To Calculate a Test Statistic Standard Deviation Known What is the sample size? If the sample is less than 30 (t-test), if the sample is larger than 30 we can apply the central limit theorem as population is approximately normally.Is the population normally distributed (z-test)?.Do you know the population standard deviation (z-test)?.Are we are working with a proportion (z-test) or mean (z-test or t-test)?.So, determining whether or not to use a z-test or a t-test comes down to four things: And depending on whether or not we know the population standard deviation will determine what type of test variable we calculate. While significance tests for population proportions are based on z-scores and the normal distribution, hypothesis testing for population means depends on whether or not the population standard deviation is known or unknown.įor a one sample t test, we compare a test variable against a test value.
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Learn the how-to with 5 step-by-step examples.Ī one sample t-test determines whether or not the sample mean is statistically different (statistically significant) from a population mean.
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Jenn, Founder Calcworkshop ®, 15+ Years Experience (Licensed & Certified Teacher)