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- A random sample of size 32 is selected from population X, and a random sample of size 43 is selected from population Y. A 90 percent confidence interval to estimate the difference in means is given as (−1.25,0.87). Consider a change in the sample sizes such that a random sample of size 52 is selected from population X and a random sample of size 63 is selected from population Y. When all other things remain the same, what effect would such a change have on the interval?A random sample of size 32 is selected from population X, and a random sample of size 43 is selected from population Y. A 90 percent confidence interval to estimate the difference in means is given as (−1.25,0.87)(−1.25,0.87). Consider a change in the sample sizes such that a random sample of size 52 is selected from population X and a random sample of size 63 is selected from population Y. When all other things remain the same, what effect would such a change have on the interval? A) The width of the interval will increase. B) The width of the interval will decrease. C) The interval will contain no negative numbers. D) The level of confidence will increase. E) The sample means will increase.Suppose that three random variables X1, X2, X3 form a random sample from the uniform distribution on interval [0, 1]. Determine the value of E[(X1-2X2+X3)2]
- A poisson random variables has f(x,3)= 3x e-3÷x! ,x= 0,1.......,∞. find the probabilities for X=0 1 2 3 4 and also find mean and variance from f(x,3).?2) Find the t-values that form the boundaries of the critical region for a two-tailed test with alpha of .05 for for n = 15A sample of 20 elements selected from a population produced a mean of 65 and a standard deviation of 9. Another sample of 25 elements selected from another population produced a mean of 58 and a standard deviation of 11. Assume that the two populations are normally distributed and the standard deviations of the two populations are equal. The null hypothesis is that the means of the two populations are equal and the alternative hypothesis is that the means of the two populations are not equal. The significance level is 5%. The critical values of t are: a. –2.014 and 2.014 b. –2.017 and 2.017 c. –1.681 and 1.681 d. –1.679 and 1.679
- Consider a hypothesis test with H 0: μ = 20 vs H 1: μ ≠ 20) at α = 0.05 on mean of a Normal population with unknown variance. If the sample variance is 4 and the true mean is 18.5, then the sample size required to obtain a power of test at least 80% is close to 15 using an appropriate OC curve. True FalseSuppose X is a random variable with standard beta distribution and parameters (alpha) = 8 and (beta) = 2 What is (PX>=0.6)?1.Random sample of size 36 were drawn with replacement from a popolation with mean and variance 0.9, and in each case the sample mean was calculated. Find the variance of X. 2.Random sample of size 9 were drawn with replacement from a popolation with mean and variance 4.2, and in each case the sample mean was calculated. Find the variance of X. 3. Random samples of size 10 are drawn with replacement from a population with mean 4 and variance 6. Let X be the sample mean. Find E(X) and Variance(X).
- We plan to run a two-tailed t-test. Our sample size is 8, and we've decided upon an alpha level of 0.01. From the t-table, what is the t critical value(s)?1. The sample mean weights for two varieties of lettuce grown for 16 days in a controlled environment are 3.259 and 1.413 and the corresponding sample standard deviations are .400 and .220. If the sample sizes for the two varieties are 9 and 6 respectively, what would be the pair of hypotheses to test if the two varieties of lettuce have the same average weight? (Given: weight of each variety of lettuce is normally distributed). A. H0: μ1 ≠ μ2 vs H1: μ1 = μ2 B. H0: μ1 = μ2 vs H1: μ1 ≠ μ2 C. H0: μ1 > μ2 vs H1: μ1 ≤ μ2 D. H0: μ1 ≤ μ2 vs H1: μ1 > μ2 2. At 5% level, what are the critical values for testing equality of mean weights in problem 1? A. 2.18 B. -2.18 and 2.18 C. -1.78 D.-1.78 and 1.78 3.What is the best decision using critical value approach in problem 1? A. The computed test statistic falls in the critical region and we do not reject the null hypothesis. B. The computed test statistic does not fall in the critical…1. The sample mean weights for two varieties of lettuce grown for 16 days in a controlled environment are 3.259 and 1.413 and the corresponding sample standard deviations are .400 and .220. If the sample sizes for the two varieties are 9 and 6 respectively, what would be the pair of hypotheses to test if the two varieties of lettuce have the same average weight? (Given: weight of each variety of lettuce is normally distributed). A. H0: μ1 ≠ μ2 vs H1: μ1 = μ2 B. H0: μ1 = μ2 vs H1: μ1 ≠ μ2 C. H0: μ1 > μ2 vs H1: μ1 ≤ μ2 D. H0: μ1 ≤ μ2 vs H1: μ1 > μ2 2.What would be the degree of freedom for the test statistic in problem 1? A. 6 B. 9 C. 12.7 D. 14 3. What would be the computed test statistic in problem 1? A. 2.93 B. 3.57 C. 8.44 D. 11.48
