Question

- Your answer is partially correct. Consider the hypothesis test Ho: Mi = U2 against H ui #uz. Suppose that sample sizes are nj = 15 and n2 = 15, thatÃj = 4.7 and X2 = 7.8 and that s = 4 and s3 = 6.20. Assume that of = oz and that the data are drawn from normal distributions. Use a = 0.05. (a) Test the hypothesis and find the P-value. (b) What is the power of the test in part (a) for a true difference in means of 3? (c) Assuming equal sample sizes, what sample size should be used to obtain ß = 0.05 if the true difference in means is – 2? Assume that a = 0.05. (a) The null hypothesis is rejected. The P-value is i 0.001 . Round your answer to four decimal places (e.g. 98.7654). (b) The power is 0.9452 Round your answer to two decimal places (e.g. 98.76). (c) nj = n2 = i 70 Round your answer to the nearest integer. Statistical Tables and Charts

Answer 1

(a) This can be easily done in R software for Statistical Analysis. The R command to find the P-value is as shown below: > install.packages ("BSDA") > library (BSDA) > tsum.test (mean.x=4.7, s.x=sqrt (4),n.x=15, mean.y=7.8, s.y=sqrt (6.20), + n.y=15, var.equal=TRUE, alternative="two.sided") Standard Two-Sample t-Test data: Summarized x and y t = -3.7593, df = 28, p-value = 0.0007981 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -4.78916 -1.41084 sample estimates: mean of x mean of y 4.7 7.8 The null hypothesis is rejected. The P-value is 0.0008.

(b) The calculation of pooled standard deviation to find the sample size and the calculation of the power is as shown below: > pooledsdc-sqrt((14*4+14*6.20)/(15+15-2)) > pooledad [1] 2.258318 > install packages ("pwr") > pwr.t.test (n=15, d = 3/2.258318, sig.level = 0.05, type = c("two.sample")) Two-sample t test power calculation n = 15 d = 1.328422 sig.level = 0.05 power = 0.9395122 alternative two.sided NOTE: n is number in *each* group Hence the power is 0.94. (c) The calculation of sample size is as shown below: > pwr.t.test(power-0.95, - -272.258318, sic.level - 0.05, type - c("two.sample")) TWO-sample t test power calculation n = 34.12784 d = 0.8856149 sig.level - 0.05 power - 0.95 alternative - two.sided each group NOTE: n is number in Hence, n = n2 = 34 If you have more questions you can send them to us and we will try our best to help you out. Good luck with your studies!!!