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Ants, bikes, & clocks: problem solving for undergraduates - download pdf or read online

By William Briggs

ISBN-10: 0898715741

ISBN-13: 9780898715743

Ants, motorcycles, and Clocks is a wonderful textual content for an undergraduate problem-solving path or as a source for arithmetic educators, delivering countless numbers of mathematical difficulties that may be utilized in any direction. Mathematically the booklet will depend on semesters of calculus, even if a lot of the publication calls for merely precalculus abilities.

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Extra resources for Ants, bikes, & clocks: problem solving for undergraduates

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The region beyond the critical value(s) must  < previous page < previous page page_64 page_65 next page > next page > Page 65 be such as to contain the least probable alpha % of all sample t, assuming the null hypothesis to be true. 4. Reject H0 if the observed sample t falls in the critical region. Up to now, we have conformed to the above steps in the following fashion. Let us assume a research hypothesis stating that some relationship between ambition and tolerance exists in the population.

If the interval does not include zero, my interval estimate of (µY2 µY1) enables me to reject the claim that (µY2 µY1) is equal to zero with 95% confidence. The more conventional teminology would have us say that we can reject the claim that (µY2 µY1) is equal to zero at the 5% level of significance, that is, with only 5% chance of error. All that is necessary to pursue this method is the known sampling distribution of the statistic "difference-of-means" plus a knowledge of where in that distribution the population parameter, (µY2 µY1), is located.

Rejecting a claim of precisely zero is, after all, not very informative. Instead, we should put ourselves in the position of saying, "I believe that there is a relationship in the population of at least such-and-such a magnitude," and then test and hope to reject the hypothesis that it is smaller. A statistically significant result in such a case would then be meaningful; it would tend to convey substantive significance, as well as statistical. Technically speaking, such a procedure is only a minor modification of the one that is commonly used.

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Ants, bikes, & clocks: problem solving for undergraduates by William Briggs

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