Question

Additional GO Tutorial Problem 9.001 A manufacturer is interested in the output voltage of a power supply used in a PC. Output voltage is assumed to be normally distributed, with standard deviation 0.25 V, and the manufacturer wished to test Ho: 9 V against H: 9 V, using n = 10 units. Statistical Tables and Charts Good. The probability of rejecting Ho when it is true is approximately 4%. (a) The critical region is x < 8.84 or X > 9.16. Find the value of a Round the answer to 3 decimal places. a T0.043 the tolerance is +/-2%

Answer 1

Hypothesis He: U = 9 against Hi! 4 $9. n=10, Standard deviation = 0: 0.25 a) The critical region is r <8.84 or d P(type I error) = P (reject Hol Ho is true) = P ( x > 9.16) x = 9.16 Pr x-u oinn 9.16-9 ) 0.25 to = = P(z ) 2.0238) 0.0214 bTrue mean output voltage is g, og v Power of tests i- ß =1-(type II error) 31-P Caccept Hol Ho is false) =1-P ( <9.16 1 el = 9.09) - | - P78 - 4 < ,6 - 1,09 ) Tolan 0,25/10 TI- P(Z < 0.8854) = 1 – 0.8120 = 0,1880 2) Hypothesis Ho: 4 =12 VIS H, : 4412 n= 4 l =12, 0 - 0.5 a) Coitical region is t < 11.5 Terror = P( reject Ho Tho is true) = p (F<11.5 1 4812) = P x l < llis -12 0,5/17

= P(Z <-2) = 0.0227 b) True mean elongation is 11:27 kg B = p (type I error) =pCaccept Ho I He is falset = P CF sllos I el = 11.27) = P( x-4 > 11,5-11,27 ) lown 0.5 Vee = P(Z > 0.92) = 0.1787 c) True mean is llis kg. B = P (type I error) = p caccept Ho I Ho is false) 2 PCF> 11.5 1 4 = 11,5) =P ( x-u >11,5-11.5) olan o.sina = P(Zso) - 0.5 Hypothesis __Ho: 02 513 vs Hi 02 #13 Level of significance d20.01 n=17 Coitical value for this test is, Karzin-t = .005,16 = 34.2671