## Statistical Analysis of High School Seniors' Goals### Problem ContextA decade-old study found that the proportion, $ p $, of high school seniors who believed that "getting rich" was an important personal goal was 70%. A researcher decides to test whether this percentage still stands. In a random sample of 245 high school seniors, 191 believe that "getting rich" is an important goal. The question is whether we can conclude, at the 0.01 level of significance, that the proportion has indeed changed.### Solution StepsPerform a **two-tailed test**. Complete the following steps with all intermediate computations carried to three or more decimal places.### Steps to Complete(a) **State the Hypotheses:**- Null Hypothesis ($ H_0 $): The proportion of high school seniors believing "getting rich" is an important goal is 70%.- Alternative Hypothesis ($ H_1 $): The proportion has changed from 70%.(b) **Determine the Type of Test Statistic:**Choose the appropriate test statistic to use from the provided options.(c) **Find the Value of the Test Statistic:**Calculate the test statistic value and round to three or more decimal places.(d) **Find the $ p $-value:**Calculate the $ p $-value, rounding to three or more decimal places.(e) **Conclusion:**Determine if the proportion of high school seniors who believe that "getting rich" is an important goal has changed:- Yes- No### DiagramsIn the provided image, there is a keypad interface to help input symbols such as:- Population mean ($ \mu $)- Population proportion ($ \sigma $)- Sample mean ($ \bar{x} $)- Sample proportion ($ \hat{p} $)These tools assist in inputting hypotheses and results for statistical calculations.Refer to the **list of formulas** if necessary to assist with calculations and hypothesis testing basics.

It is given that among the 245 high school seniors in his random sample 191 believe that "getting…

Answered: A decade-old study found that the…

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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