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Chapter 10 Section 1 Additional Problem 1 Your answer is partially correct. Try again. Consider the hypothesis test Ho: Mi = 12 against HL M1 <uz with known variances al = 9 and 62 = 5. Suppose that sample sizes n = 9 and n2 = 15 and that = 14.3 and 22 = 19.5. Use a = 0.05. (a) Test the hypothesis and find the P-value. (b) What is the power of the test in part (a) if u is 4 units less than 2? (c) Assuming equal sample sizes, what sample size should be used to obtain B = 0.05 if mi is 4 units less than u2? Assume that a = 0.05. (a) The null hypothesis is not rejected. The P-value is 0.0557 Round your answer to four decimal places (e.g. 98.7654). 0.35665 (b) The power is Round your answer to two decimal places (e.g. 98.76). 67 (c) n = 12 Round your answer up to the nearest integer.

Answer 1

Solution:

Given that: consider the hypothesis test Ho: Mis My against Ho: Medy With Known Variances, 09 02 = 5 Sample sizes 1,79 na = 15 14.3 And that xi х, 19.5 d = 0.05 forca):- * The pooled variance is given by 02.0? 2 +02 ne > at > 89 ។ + 25 15 => 10.667 3.266 * the test statistic' is given by Xi - Xe Z => 14.3-19.5 3.266 => -1.592 The P-value P(Z <-1.592) < 0.0557 Thus at level 2-0.05, we fail to reject the null hypotesis forcoji- under Ho and at the level 2.0.05 We reject the null hypothesis if Zx-1.645 →P G Vice ។ < -1.645+ 3.266 3.266 to)

=> PC Z < -1.645 + 3.266 오 -> 0.9222 for cc): * We assume equal sample size then the pooled variance ib, 02.106 power test at 2:0.05 is X-X2+4 P Xiaxe < 1.645 ( . <-1.645+ Top 106 lor -). 645 + un 1,645 105 In 2x 1.6451100 ។ => 8.468 n. 71.7 Therefore, Nearest integer is 0-71