Calculate the Welch’s t-statistic As you may recall from the one sample module, the general form of a test statistic is: In the case of two independent samples, our estimate is the difference between the two sample means. The standard deviations are given in the problem (400 g (Neuse) and 300 g (Tar Pam)).Ĩ. Calculate standard deviation of sample IF using a t-test. The mean weight of Tar Pamlico crabs is 700 grams, while the mean weight of the Neuse crabs is 800 grams.ħ. The sample means are given in this problem. If the sample size is large enough, the t-distribution will approximate the normal distribution.Ħ. Therefore it is most appropriate to use a t-test in this example. We do not know the true standard deviations of the weights of the crabs in the two basins. Decided whether a z-statistic or t-statistic is appropriate. Please note that the population parameters are used in the hypotheses and NOT the sample statistics.ĥ. The null hypothesis should cover all other possible outcomes. Ho: µ neuse – µ tarpamlico ≤ 0 Ha: µ neuse – µ tarpamlico > 0īecause we want to test if the Neuse crabs are larger than the crabs in the Tar Pamlico basin, we set the alternative hypothesis to state that the mean weight of crabs in the Neuse minus the mean weight of TP crabs is greater than zero. Establish null and alternative hypotheses. Examine the appropriateness of a comparison of means test (based on the assumptions)***. This is a one-sided test in which we hypothesize that the crabs in the Neuse will weigh more than the crabs in the Tar Pamlico basin. We will use the Welch’s t-test which does NOT require the assumption of equal variance between populations. This problems illustrates a two independent sample test. A side-by-side boxplot of the two samples is shown below.ġ. The mean weight of the Neuse crabs is 800 grams with a standard deviation of 400 grams (s n). The mean weight of the Tar Pamlico crabs is 700 grams with a standard deviation of 300g (s tp). We randomly sample 100 blue crabs in each basin. Based on the health of the two rivers, we believe that the crabs in the Neuse will be larger, on average, and would like to test for this effect. For this problem, we want to compare the average weights of blue crabs in two river basins: (1) Tar-Pamlico and (2) Neuse River. To conduct a two independent sample comparison of means test, you follow very similar steps as described in the one sample test with some modifications.
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