Question below... True or false: There is evidence, at 伪 = 0.01, to reject the null hypothesis, H0: 渭 > 1150

A manufacturer of light bulbs claims that his light bulbs have a mean life, m , of 1150 or more hours with a standard deviation of 80 hours. A random testing of 36 light bulbs yielded a mean of 1125 hours.








True or false: There is evidence, at 伪 = 0.01, to reject the null hypothesis, H0: 渭 %26gt; 1150











True





FalseQuestion below... True or false: There is evidence, at 伪 = 0.01, to reject the null hypothesis, H0: 渭 %26gt; 1150
False.





If X is distributed N(1150, 80^2) then X1 + ... + X36 is distributed N(36 * 1150, 36 * 80^2) and so (X1 + ... + X36)/36 is distributed as N((36 * 1150)/36, (36 * 80^2)/36^2) or N(1150, 80^2 / 36) = N(1150, (80/6)^2) = N(1150, (40/3)^2).





So the corresponding Z-score for (X1 + ... + X36)/36 = 1125 is z = (1125 - 1150) / (40/3) = -75/40 = -1.875. The critical values at 伪 = 0.01 are +/- z = 2.33 (one-sided) and +/- z = 2.58 two-sided. To reject H0: 渭 %26gt; 1150 at 伪 = 0.01 would have required a measured Z-score of -2.33 or less, so we do not reject H0 at 伪 = 0.01.





DanQuestion below... True or false: There is evidence, at 伪 = 0.01, to reject the null hypothesis, H0: 渭 %26gt; 1150
false