9.2.6 A random sample of n = 15 is tested and x̅ = 2.78. It is known that σ = 0.9 and that X is

Question

9.2.6 A random sample of $n = 15$ is tested and $\bar{x} = 2.78$. It is known that $\sigma = 0.9$ and that $X$ is normally distributed. a. Test $h_0: \mu = 3$ versus $h_1: \mu \neq 3$ using $\alpha = 0.05$. b. What is the power of this test if $\mu = 3.25$? c. What sample size would be required to detect a true mean of 3.75 if we wanted the power to be at least 0.9?

          9.2.6 A random sample of $n = 15$ is tested and $\bar{x} = 2.78$. It is known that $\sigma = 0.9$ and that $X$ is normally distributed.
a. Test $h_0: \mu = 3$ versus $h_1: \mu \neq 3$ using $\alpha = 0.05$.
b. What is the power of this test if $\mu = 3.25$?
c. What sample size would be required to detect a true mean of 3.75 if we wanted the power to be at least 0.9?

9.2.6 A random sample of n = 15 is tested and x̅ = 2.78. It is known that σ = 0.9 and that X is normally distributed.
a. Test h0: μ = 3 versus h1: μ≠ 3 using α = 0.05.
b. What is the power of this test if μ = 3.25?
c. What sample size would be required to detect a true mean of 3.75 if we wanted the power to be at least 0.9?

Added by Victor F.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sri K

12/13/2022

Step 1

Step 1: The null hypothesis is $H_0: \mu = 3$ and the alternative hypothesis is $H_1: \mu \neq 3$. Show more…

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9.2.6 A random sample of n = 15 is tested and $\bar{x}$ = 2.78. It is known that σ = 0.9 and that X is normally distributed. a. Test $h_0$: μ = 3 versus $h_1$: μ ≠ 3 using α = 0.05. b. What is the power of this test if μ = 3.25? c. What sample size would be required to detect a true mean of 3.75 if we wanted the power to be at least 0.9?