Run A Hartley Test Use 050

Run A Hartley Test Use 050

1. (30pts) Problem 8.2.6, page 332. a. Run a Hartley test, use 05.0ï€½ï¡ . b. If you accept ð»ð‘œ in a, run an ANOVA, use 05.0ï€½ï¡ . c. If you reject ð»ð‘œ in b, do the Tukey test, use 05.0ï€½ï¡ . 2. (5pts) Suppose the weights W (kg) of a male population is normally distributed. If we know ð‘ƒ(𑊠≤ 70) = 0.65, and ð‘ƒ(𑊠≤ 50) = 0.35. Now from this population, 15 males are randomly selected, what is the probability that at least 3 of them weigh more than 65kg? 3. (5pts) If after a Tukey test (𑘠populations), and you reach the statistical conclusion that ðœ‡ð‘– ≠ðœ‡ð‘— , use what you have learned from this class to verify that the confidence interval for ðœ‡ð‘– − ðœ‡ð‘— is the following (ð‘¥ð‘– − ð‘¥ð‘— ) − # ∙ ð‘€ð‘†ð‘Š ∙ ð‘›ð‘– + 1 ð‘›ð‘—

Paper For Above instruction

The assignment encompasses several advanced statistical tests and analyses, starting with the execution of a Hartley test to evaluate the homogeneity of variances across multiple groups. Following this, it involves conducting an ANOVA to compare group means if the variances are deemed homogeneous. Should the ANOVA indicate significant differences, a Tukey post-hoc test is necessary to identify specific group differences. Additional questions explore probabilities within a normal distribution, confidence interval derivations, hypothesis testing, and specific statistical formulas for variances and means under various assumptions.

Initially, the task requires performing a Hartley test using a significance level of 0.05 on a dataset specified in problem 8.2.6, page 332. This test assesses whether the variances across different groups are equal, which is a crucial prerequisite for valid ANOVA results. If the Hartley test supports the assumption of equal variances (failure to reject the null hypothesis), the next step involves conducting an ANOVA at the same significance level to determine whether there are significant differences among group means.

If the ANOVA results lead to rejection of the null hypothesis that all group means are equal, a Tukey test is employed to pinpoint which groups differ markedly. The problem provides the specific confidence level (95%) for the Tukey test, which guides the identification of pairwise differences between group means. Conversely, if the ANOVA does not reject the null hypothesis, the analysis concludes that the means are statistically similar, and no further pairwise testing is necessary.

The next set of problems extends into probability theory within a normal distribution context. Given the cumulative distribution information that P(W ≤ 70) = 0.65 and P(W ≤ 50) = 0.35, we evaluate the probability that, in a random sample of 15 males, at least 3 weigh more than 65 kg. This involves understanding the underlying distribution parameters and applying binomial probability models or normal approximations as appropriate.

The assignment also delves into constructing confidence intervals for population means based on multiple samples. When assessing the results of a Tukey test, the formulas for confidence intervals depend on sample means, variances, and degrees of freedom derived from the t-distribution. Determining the exact degrees of freedom involves understanding the combined variance estimates and sample sizes.

Furthermore, the tasks include hypothesis testing of population means with unknown variances, employing pooled variance formulas when standard deviations are equal or modified formulas when one variance is a multiple of the other. These require precise application of t-tests or relevant formulas under specified conditions.

Additional questions examine the level of significance in statistical tests, requiring the calculation of critical values (k) to achieve a specified significance level (e.g., 0.05), as well as sample size determination based on variance bounds to ensure desired power.

The complexities extend to modeling the probability that a cell maintains a specific form over a period, modeled as a Markov process, with probabilities of staying or changing form. Computing the probability of the cell being in a particular form after 30 days involves understanding and applying the properties of the Markov chain.

Lastly, the assignment references a specific problem from a textbook section (Problem 12.4.6, page 629), indicating the need to apply concepts from that problem in the context of these analyses. Overall, the assignment integrates hypothesis testing, confidence interval estimation, probability calculations, and Markov processes within a comprehensive statistical framework.

References

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