hw10sol_fall03 - AMS 310.01 FALL 2003 Homework #10...

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Unformatted text preview: AMS 310.01 FALL 2003 Homework #10 Solutions 7.30 (a) The probability of Type I error is the probability that X is less than 2.9960 or greater than 3.0040 when 3.0000 = . Using a normal approximation to the distribution of the sample mean, this probability is given by 2.9960 3.0000 3.0040 3.0000 ( ) 1 ( ) 0.0250 / 30 0.0250 / 30 F F-- + - ( 0.876) 1 (0.876) 2 ( 0.876) 0.381 F F F =- + - =- = (b) The probability of type II error is the probability that 2.9960 3.0040 X < < when 3.0050 = . Using a normal approximation, this probability is given by 3.0040 3.0050 2.9960 3.0050 0.0250 / 30 0.0250 / 30 F F--- ( 0.219) ( 1.97) 0.4133 0.0244 0.3889 F F =--- =- = 7.32 Using the normal approximation for the distribution of the sample mean, we need to find x such that 100 0.01 12 / 40 x F- = Using the normal table, we see that 100 2.33 12 / 40 x- = - So, we reject the null hypothesis if...
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hw10sol_fall03 - AMS 310.01 FALL 2003 Homework #10...

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