Part b show the change. change null hypotheseis x >14 to what is in red in Part b. find reject and excepted for x>15 and x<=15.recaluate alpha and beta The image contains text related to hypothesis testing using a binomial distribution:```alpha = P(reject H0 | H0 is true) = P(X ≤ 14 | theta = 0.9) =beta = P(accept H0 | H1 is true) = P(X > 14 | theta = 0.6) =H0: theta = 0.9H1: theta = 0.6X ~ Bin(n = 20, theta)accept: X > 14 => X = 15, 16, 17, 18, 19, 20reject: X ≤ 14 X = 0, 1, 2, ... , 14```Below is an incomplete section for computing decision rules and error probabilities:```accept: X > 15reject: X ≤ 15alpha =beta =``` **Statistical Hypothesis Testing Example**In testing a new medication, the manufacturer wants to evaluate the null hypothesis \(\theta = 0.90\) against the alternative hypothesis \(\theta = 0.60\). The test statistic \(X\) represents the observed number of successes (recoveries) in 20 trials. If \(x > 14\), the null hypothesis is accepted; otherwise, it is rejected.**Solution:**1. **Acceptance Region:** - The acceptance region for the null hypothesis is \(x = 15, 16, 17, 18, 19,\) and \(20\).2. **Rejection Region (Critical Region):** - The rejection region, also known as the critical region, is \(x = 0, 1, 2, \ldots, 14\).3. **Calculating \(\alpha\) and \(\beta\):** - **\(\alpha\)** (Type I Error Probability): \[ \alpha = P(X \leq 14; \theta = 0.90) = 0.0114 \] - **\(\beta\)** (Type II Error Probability): \[ \beta = P(X > 14; \theta = 0.60) = 0.1255 \]In this testing scenario, \(\alpha\) indicates the probability of rejecting the null hypothesis when it is true, while \(\beta\) represents the probability of failing to reject the null hypothesis when the alternative is true.

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Answered: Part b show the change. change null…

Part b show the change. change null hypotheseis x >14 to what is in red in Part b. find reject and excepted for x>15 and x<=15. recaluate alpha and beta

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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