5. Suppose there are 2 populations, each with mean ₁ and ₂ and standard deviation of ₁ and ₂ respectively. The interest is to measure a random variable X by taking a random sample of size n from the first population. In a similar manner, another random variable Y is measured by independently taking a random sample of size m from the second population. Assuming n and m are sufficiently large, then demonstrate the following properties: X~N (μ₁, 1) b. Y~N (μ₂, 1) a. c. (X-Ỹ)-N (1²₂-1 H₂, 11 + E

Really need it to study, please don't copy the answers from others.

1. A study compared the number of tree species in unlogged forest plots to similar plots logged 8 years earlier. Independent random samples of both logged and unlogged plots were analyzed and the number of tree species was recorded. Tables 1 and 2 present the Shapiro-Wilk normality test for both types of forest plots and the Independent Samples t-test results. Use the information presented in these tables to answer the questions. Table 1: Tests of Normality Tests of Normality Kolmogorov-Smirnov Shapiro-Wilk Forest Plot Statistic df Sig. Statistic df Sig. Tree_Species Logged .181 12 .200 .936 12 .444 Unlogged .110 14 .200 .945 14 .480 *. This is a lower bound of the true significance. a. Lilliefors Significance Correction Table 2: Independent Samples Test Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means 95% Confidence Interval of the Difference Mean Std. Error F Sig. t df Sig. (2-tailed) Difference Difference Lower Upper Equal variances…

Let x be a random variable that has a distribution with mean μ = 150 and standard deviation σ = 15.3. For samples of size n = 36   the sampling distribution of  i s with mean = and standard deviation = .