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
4.4106 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)
Math question: What is the value of sin(45 degrees) + cos(30 degrees)?
+
What is the value of 2 raised to the power of 5 multiplied by the square root of 16, all divided by 4?
+
What is the value of 5 to the power of 3 multiplied by the square root of 16, divided by 2?
+
New questions in Mathematics