Question
0. Suppose that we know the standard deviation of a population is σ = 10, and we’re testing the following hypothesis using a sample size of 100: H0 : µ = 25 H1 : µ ̸= 25 If the actual population mean was µ = 26 what is the probability that we make a Type II error at a level of significance of α = 0.1?
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Answer to a math question 0. Suppose that we know the standard deviation of a population is σ = 10, and we’re testing the following hypothesis using a sample size of 100: H0 : µ = 25 H1 : µ ̸= 25 If the actual population mean was µ = 26 what is the probability that we make a Type II error at a level of significance of α = 0.1?
Adonis
4.495 Answers
the critical value is \pm 1.645
type II error means, we fail to reject the null hypothesis and the null hypothesis is false
do not reject the null hypothesis if
-1.645 < Z < 1.645
-1.645 < \frac{\bar{x}-25}{10/\sqrt{100}} < 1.645
23.355 < \bar{x} < 26.645
the probability that we make type II error is
P(23.355 <\bar{x} < 26.645 | \mu =26)
=P(Z < \frac{26.645-26}{10/\sqrt{10}})-P(Z < \frac{23.355-26}{10/\sqrt{10}})
=P(Z < 0.645)-P(Z < -2.645)
=0.7405-0.0041
=0.7364
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