### Investor Confidence Hypothesis TestingA well-known brokerage firm executive claimed that at least 50% of investors are currently confident of meeting their investment goals. An XYZ Investor Optimism Survey, conducted over a two-week period, found that out of 86 randomly selected people, 47 of them said they are confident of meeting their goals.#### Hypothesis TestingSuppose you have the following null and alternative hypotheses for a test you are running:- **Null Hypothesis (H₀):** \( p = 0.5 \)- **Alternative Hypothesis (Hₐ):** \( p > 0.5 \)#### Calculation of the Test StatisticTo determine whether the proportion of confident investors is significantly greater than 0.5, we calculate the test statistic. The calculation is based on the sample proportion and the population proportion provided in the hypotheses.Use the formula for the test statistic (z):\[ z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0 (1 - p_0)}{n}}} \]Where:- \( \hat{p} \) is the sample proportion- \( p_0 \) is the population proportion under the null hypothesis- \( n \) is the sample sizePlug in the values:- \( \hat{p} = \frac{47}{86} \)- \( p_0 = 0.5 \)- \( n = 86 \)The formula now becomes:\[ z = \frac{\frac{47}{86} - 0.5}{\sqrt{\frac{0.5 (1 - 0.5)}{86}}} \]Calculate the test statistic, rounded to 3 decimal places:\[ z = \]*(The user is expected to fill in the calculated value.)*#### Input AreaTo complete the test, enter the calculated test statistic in the box provided and click the "Check Answer" button to see if your computation is correct.```plaintextz = [__]```*Note: The detailed calculations and interpretations are essential to formally conclude the hypothesis testing.*

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Answered: A well-known brokerage firm executive…

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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