Let X and Y in the correct forms kindly

A federal law requires periodic testing in standard subjects. A random sample of 63 junior high school students from a certain city was selected, and each student's scores on a standardized mathematics examination and a standardized English examination were recorded. School administrators were interested in the relationship between the two scores. Suppose the correlation coefficient for the two examination scores is 0.82. Complete parts a and b below. Use a = 0.10 where needed. a. Provide an explanation of the sample correlation coefficient in this context. Fill in the blank below. There appears to be correlation between the standardized mathematics examination and the standardized English examination for these students. b. Using a level of significance of a =0.10, test to determine whether there is a positive linear relationship between mathematics scores and English scores for junior high school students in the city. What are the appropriate null and alternative hypotheses to test for a positive linear relationship? OA Hip0 HA: P20 Haipso O C. Ho: p20 OD. Hipso HaiPED HA: PEO OE. Ho: p=0 OF. Ho: PRO1. (24 points) In baseball, a batting average is obtained by dividing hits by at-bats. Is there evidence that team batting average is positively correlated with the number of team wins? The hypotheses are Ho : p =0 Ha: p>0 My sample data came from the 30 Major League Baseball teams in 2016, I found that r = 0.340. Assume that the a = 0.05 significance level will be used. (a) (6 points) Where would a randomization distribution be centered? Randomized Distributions are centered around the Null Value = 0 (b) (6 points) Where would a bootstrap distribution (for the confidence interval) for the correlation be centered? (c) (6 points) The p-value for the hypothesis test is 0.032. Interpret the p-value. (d) (6 points) State the conclusion of the test in context using the a = 0.05 significance level.Let X1, X2, ..., Xn be a random sample from a population with mean #1 and variance 0'2 and Y 1, Y2, ..., Y m be an independent random sample from another population with mean #2 and variance 0'2. Let 2? and 17 be the sample means of the two random samples, and SE and 8% the sample variances. (a) Show that I? 17 is an unbiased estimator of,u1,u2. _ 2 _ 2 (b) Show that $5 = W is an unbiased estimator of 02. (c) If the two populations are both normal, then what is the sampling distribution of X Y? If the two populations are not normal, what can you say about the sampling distribution of X 17? (d) If the two populations are normal, argue that I? -17-(#1-#2) Sp,/1+1/m follows a 1' distribution with n + m 2 degrees of freedom