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He wants to know if there is a significant difference between the mean number of cavity trees in the Adirondack Park and the old growth stands in the Monongahela National Forest. This makes the test more conservative, requiring more evidence to reject the null hypothesis.Ī forester is studying the number of cavity trees in old growth stands in Adirondack Park in northern New York. This method results in a smaller value for degrees of freedom and therefore a larger critical value. This test statistic follows the student’s t-distribution with the degrees of freedom adjusted byĪ simpler alternative to determining degrees of freedom when working a problem long-hand is to use the lesser of n 1-1 or n 2-1 as the degrees of freedom. The test statistic is Welch’s approximation (Satterthwaite Adjustment) under the assumption that the independent population variances are not equal. Rewriting the null hypothesis of μ 1 = μ 2 to μ 1 – μ 2 = 0, simplifies the numerator. We will also use the same three pairs of null and alternative hypotheses. The populations must be normally distributed, or both have large enough sample sizes (n 1 and n 2 ≥ 30). Both samples come from independent random samples. The assumptions we saw in Chapter 3 still must be met.
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Is the proportion of people who support alternative energy in California greater compared to New York?.
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You want to determine if the treatment used in Skaneateles Lake has reduced the number of milfoil plants over the last three years.You are studying turkey habitat and want to see if the mean number of brood hens is different in New York compared to Pennsylvania.This chapter deals with inferences about two means, proportions, or variances. Frequently, we need to compare two sets of data, and make inferences about two populations. In both of these chapters, all the examples involved the use of one sample to form an inference about one population. We have used sample data to construct confidence intervals to estimate the population mean or proportion and to test hypotheses about the population mean and proportion. Up to this point, we have discussed inferences regarding a single population parameter (e.g., μ, p, σ 2).