Question

Let $X_{1}, X_{2}, \ldots, X_{n}$ denote a random sample from a normal distribution $N(\theta, 16)$. Find the sample size $n$ and a uniformly most powerful test of $H_{0}: \theta=25$ against $H_{1}: \theta<25$ with power function $\gamma(\theta)$ so that approximately $\gamma(25)=0.10$ and $\gamma(23)=0.90$.

Name: Let X1, X2, …, Xn denote a random sample from a normal distribution N(θ, 16). Find the sample size n and a uniformly most powerful test of H0: θ=25 against H1: θ<25 with power function γ(θ) so that approximately γ(25)=0.10 and γ(23)=0.90.
Uploaded: 2023-11-29T20:27:09-08:00
Duration: 4 min 19 s
Channel: Luke Humphrey
Description: Let X1, X2, …, Xn denote a random sample from a normal distribution N(θ, 16). Find the sample size n and a uniformly most powerful test of H0: θ=25 against H1: θ<25 with power function γ(θ) so that approximately γ(25)=0.10 and γ(23)=0.90.

          Let $X_{1}, X_{2}, \ldots, X_{n}$ denote a random sample from a normal distribution $N(\theta, 16)$. Find the sample size $n$ and a uniformly most powerful test of $H_{0}: \theta=25$ against $H_{1}: \theta<25$ with power function $\gamma(\theta)$ so that approximately $\gamma(25)=0.10$ and $\gamma(23)=0.90$.

Added by Jason O.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Luke Humphrey

11/29/2023

Step 1

We know that the test statistic for a normal distribution with known variance is given by: $$Z = \frac{\bar{X} - \theta}{\frac{\sigma}{\sqrt{n}}}$$ where $\bar{X}$ is the sample mean, $\theta$ is the population mean, $\sigma$ is the population standard Show more…

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Let $X_{1}, X_{2}, \ldots, X_{n}$ denote a random sample from a normal distribution $N(\theta, 16)$. Find the sample size $n$ and a uniformly most powerful test of $H_{0}: \theta=25$ against $H_{1}: \theta<25$ with power function $\gamma(\theta)$ so that approximately $\gamma(25)=0.10$ and $\gamma(23)=0.90$.