![]() ![]() We calculate the average for the sample and then calculate the difference with the population mean, mu: If we cannot reject the null hypothesis, then we make a practical conclusion that the labels for the bars may be correct. If we can reject the null hypothesis that the mean is equal to 20 grams, then we make a practical conclusion that the labels for the bars are incorrect. We are testing if the population mean is different from 20 grams in either direction. The labels claiming 20 grams of protein would be incorrect. The alternative hypothesis is that the underlying population mean is not equal to 20. Our null hypothesis is that the underlying population mean is equal to 20. Let’s look at the energy bar data and the 1-sample t-test using statistical terms. We make a practical conclusion that the labels are incorrect, and the population mean grams of protein is greater than 20. Since 3.07 > 2.043, we reject the null hypothesis that the mean grams of protein is equal to 20. We compare the value of our statistic (3.07) to the t value. The most likely situation is that you will use software and will not use printed tables. Most statistics books have look-up tables for the distribution. The critical value of t with α = 0.05 and 30 degrees of freedom is +/- 2.043. For the energy bar data:ĭegrees of freedom = $ n - 1 = 31 - 1 = 30 $ The degrees of freedom are based on the sample size. For a t-test, we need the degrees of freedom to find this value. We find the value from the t-distribution based on our decision. In practice, setting your risk level (α) should be made before collecting the data. For the energy bar data, we decide that we are willing to take a 5% risk of saying that the unknown population mean is different from 20 when in fact it is not. We decide on the risk we are willing to take for declaring a difference when there is not a difference.To make our decision, we compare the test statistic to a value from the t-distribution. The figure below shows a histogram and summary statistics for the energy bars. We decide that the t-test is an appropriate method.īefore jumping into analysis, we should take a quick look at the data. We assume the population from which we are collecting our sample is normally distributed, and for large samples, we can check this assumption.We assume the energy bars are a simple random sample from the population of energy bars available to the general consumer (i.e., a mix of lots of bars).A sample from a single lot is representative of that lot, not energy bars in general. An example of dependent values would be if you collected energy bars from a single production lot. The grams of protein in one energy bar do not depend on the grams in any other energy bar. Let’s start by answering: Is the t-test an appropriate method to test that the energy bars have 20 grams of protein ? The list below checks the requirements for the test. ![]()
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