Question

A fisherman claims that the mean breaking strength of his fishing line is 15 kg with a standard deviation of 500 g. To test the hypothesis that u = 15 kg against the alternative that p < 15 kg, a random sample of 50 of his fishing lines will be tested. With the critical region is defined to be x < 14.9, find the probability of committing a type Il error for u = 14.9.

Answer 1

500g=0.5kg

$\beta$ =type two error

std error =std deviation/(n)^1/2 =0.5/(50)^1/2=0.0707

for $\mu$ =14.9

$\beta$ =P(X>14.9)=P(Z>(14.9-14.9)/0.0707)=P(Z>0.0)=0.5