The image presents a hypothesis testing problem related to SAT scores. ### Problem Statement:The mean SAT score in mathematics is 558 with a standard deviation of 36. A special preparation course claims that the mean SAT score of its graduates is greater than 558. An independent researcher tests this claim using a random sample of 50 students who completed the course; the mean SAT score for this sample was 569. At the 0.05 level of significance, the question is whether the population mean SAT score for course graduates is greater than 558, assuming the population standard deviation for course graduates is also 36.### Steps to Perform a One-tailed Test:#### (a) State the Hypotheses:- **Null Hypothesis (H₀):** The mean SAT score is 558 (H₀: μ = 558).- **Alternative Hypothesis (H₁):** The mean SAT score is greater than 558 (H₁: μ > 558).#### (b) Determine the Type of Test Statistic:- Choose a z-test for means as the population standard deviation is known.#### (c) Calculate the Test Statistic:- The test statistic formula for a mean is: \[ z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}} \] where \(\bar{x}\) is the sample mean, \(\mu\) is the population mean, \(\sigma\) is the standard deviation, and \(n\) is the sample size.#### (d) Find the P-value:- Enter the calculated z-value to find the p-value from a z-table or statistical software.#### (e) Conclusion: - Decide if the preparation course's claim can be supported.- **Options:** Yes or No#### List of Symbols:A diagram shows various statistical symbols and their representations (e.g., \(\mu\), \(\sigma\), \(\bar{x}\), etc.) useful for conducting hypothesis tests.### Conclusion:Follow the steps using the provided data to decide whether to reject the null hypothesis, thus supporting the course's claim that its graduates have a higher SAT score mean than 558.

Given,sample size(n)=50sample mean(x¯)=569population standard deviation(σ)=36α=0.05

Answered: The mean SAT score in mathematics is…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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