Question

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Q6) 2 points For testing Ho: u = 14, H:H # 14, an a = 0.05 level t-test is being considered. What sample size is necessary in order for the probability to be 0.1 of falsely failing to reject H, when the true population mean differs from 14 by 0.5? From a preliminary sample we estimate o to be 1.25.

Answer 1

Solution for giren Problem: - Given that, The following hypothesis to be tested Hol=14 Hi: MF 14 we need to find the sample size neccessary in order for the probability to be 0.1 or fallely failing to reject to when the true population mean differs from 14 by 0.5. The population standard deviation is 1.25. The level of Significence is x=0.05. The hypothesis test û two tailed test and so the formula for estinating the sample size required to achieve (1-P) powers of test at a level of significance and the true mean difference s is given Zan+2p) v below. n - S The probability of falsely failing to reJet Ho is the type II enor and it is on. In this case. It is denoted as ß. So it is the complement of the powe of the test. The following are the information to be used. x=0.05 ß = 0.1 8=0.5 T = 1.25 Substitute the above values in the formula for the sample size. (2«12+Zp) 20.025 +2.1)*(1.2.57" (0.5)~ 2 sr

Hence solved, please upole, Think your (1.96+1.2816)^(1.25) 66.67 (0.57 Sample size of at least 66 in neccessary in order for the Pobability to be 0.1 of falsely failing to se Jeet ♡ differs from it by o.s. When the true population meen