of interest and o are known. Let 7(k) be the value of the sample mcan of an aple of size ng from N(µk,0) for k 1,..., K. Let c1,..., Ck be the specificd n) constants. cuct a 95% confidence interval for ciµi + ……·+ ck#K•

4.52 Random variables X and Y follow a joint distribution f(x, y) = = 2, 0< x≤y< 1, otherwise. 0, Determine the correlation coefficient between X and Y.

Calculate the test-statistic, t with the following information for a Two Independent Samples t Test with Ha:μ1-μ2≠0. Be sure to first determine if you need to pool or not.n1=60, ¯x1=2.53, s1=0.53n2=50, ¯x2=2.69, s2=0.96Round to 3 decimal places. t =__________ It is pool or not?________

A random sample of 9 size AA batteries for toys yield a mean of 3.66 hours with standard deviation, 1.05 hours. (a) Find the critical value, t, for a 99% CI. t =  (b) Find the margin of error for a 99% CI.

A population has a mean µ = 161 and a standard deviation o = 20. Find the mean and standard deviation of the sampling distribution of sample means with sample size n = 56. The mean is = μx (Round to three decimal places as needed.) and the standard deviation is o- = X 3 X

A random sample of 11 size AA batteries for toys yield a mean of 2.98 hours with standard deviation, 1.19 hours. (a) Find the critical value, t?/2, for a 99% CI. ??/2 = (b) Find the margin of error for a 99% CI.

Past research has indicated that the average age of death row inmates is 41 years old. researcher would like to determine if the average age has changed. She randomly selects 50 death row inma s and ds their average age to be 37 years old. The hypothesis the statistician wants to test is: a. Ho: µ=37 vs_ Ha: µ ± 41. b. Ho: µ=41 vs Ha: µ< 41. Ho: u = 41 vs. H: u 41 d. Ho: µ=37 vs_Ha: µ< 41. C. 2. If a player at a casino is playing roulette and betting on red, there is a 18 / 38 or 0.474 chance that he will win on any spin of the roulette wheel. If we take a random sample of 300 players betting on red, then p is the proportion of times that the player wins. What is the mean of the sampling distribution of p? t' a. b. What is the standard deviation (os) of the sampling distribution of p? c. If repeated samples of 300 players are taken, what would be the range of the sample proportion of players victories according to the 95 part of the 68-95-99.7 rule" pts) 3. The z statistic for a…

Medical Operations The director of a medical hospital feels that her surgeons perform fewer operations per year than the national average of 211. She selected a random sample of 15 surgeons and found that the mean number of operations they performed was 209.3. The standard deviation of the sample was 3.8. Is there enough evidence to support the director's feelings at =α0.01? Assume that the population is approximately normally distributed. Use the critical value method and tables.

= You wish to test Ho: d 0 versus Ha: Md > 0 at a significance level of 0.10. For the context of this problem, d = μ2 μ₁ where the first data set represents a pre-test and the second data set represents a post-test. You obtain pre-test and post-test samples for nd 18 subjects. The average difference -= (post-pre) is d 3.8 with a standard deviation of the differences of sa 32.6. Round your answers to three decimal places, and round any interim calculations to four decimal places. What is the test statistic? - - -