Question

Suppose the null hypothesis is H_o : µ = 500 against H_a : > µ = 500 , and the significance level for this testing is 0.05. The population in question is normally distributed with standard deviation 100. A random sample of size n=25 will be used. If the true alternative mean is 550, then the probability of committing the type II error is ____.

Answer 1

Hypothesized mean true mean standard deviation sample size standard error of mean for 0.05 level and right tailed test critival value Ζα rejection region:x>-μ+Za*ox or type Il error -probability of not rejecting B P(Z 500 550 En 25 532.8971 (532.8971 ua)/ox)) -P(Z -0.86) 0.1949

from above :

probability of committing the type II error is =0.1949