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?
192
likes962 views
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
4.4105 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
Frequently asked questions (FAQs)
What is the Pythagorean theorem used to calculate?
+
What is the length of the altitude of an equilateral triangle with side length 10?
+
What is the volume of a rectangular solid with length L, height H, and width W? (
+
New questions in Mathematics