**Hypothesis Testing in Corporate Acquisitions**A business journal conducted an investigation to study the performance and timing of corporate acquisitions. The investigation focused on a random sample of 2,893 firms, out of which 759 firms announced one or more acquisitions during the year 2000. The goal is to determine whether this sample provides sufficient evidence to infer that the true percentage of all firms that announced one or more acquisitions during the year 2000 is less than 28%. The significance level (α) for this test is set at 0.05.**Hypotheses:**1. \[ \text{Null Hypothesis (H}_0\text{): p = 0.28} \]2. \[ \text{Alternative Hypothesis (H}_a\text{): p < 0.28} \]**Rejection Region:**To determine the rejection region for this hypothesis test, we look for the critical value associated with the significance level (α = 0.05). For a left-tailed test: - Critical z-value = -1.645\[ \boxed{ \text{A. } z < -1.645} \]**Calculate the z-statistic:**To proceed with the hypothesis test, we calculate the value of the z-statistic using the formula for sample proportions:\[z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0 (1 - p_0)}{n}}}\]where:- \(\hat{p}\) is the sample proportion.- \(p_0\) is the hypothesized population proportion.- \(n\) is the sample size.Given data:- \[ \hat{p} = \frac{759}{2893} \approx 0.262 \]- \[ p_0 = 0.28 \]- \[ n = 2893 \]Substitute these values into the formula:\[z = \frac{0.262 - 0.28}{\sqrt{\frac{0.28 \times (1 - 0.28)}{2893}}}\]Calculate the z-statistic (rounding to two decimal places as needed):\[z = \boxed{}\]

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A business journal investigation of the performance and timing of corporate acquisitions discovered that in a random sample of 2,893 firms, 759 announced one or more acquisitions during the year 2000. Does the sample provide sufficient evidence to indicate that the true percentage of all firms that announced one or more acquisitions during the year 2000 is less than 28%? Use a = 0.05 to make your decision. H: p#0.28 H3: p>0.28 O.C. Ho: p#0.28 H: p= 0.28 O D. Ho: p>0.28 H: ps0.28 OF. Ho: p<0.28 H3: p= 0.28 E. Ho: p=0.28 Ha: p<0.28 What is the rejection region? Select the correct choice below and fill in the answer box(es) to complete your choice. (Round to three decimal places as needed.) O A. z< -1.645 O B. z> O C. z< or z> Calculate the value of the z-statistic for this test. (Round to two decimal places as needed.)

A business journal investigation of the performance and timing of corporate acquisitions discovered that in a random sample of 2,893 firms, 759 announced one or more acquisitions during the year 2000. Does the sample provide sufficient evidence to indicate that the true percentage of all firms that announced one or more acquisitions during the year 2000 is less than 28%? Use a = 0.05 to make your decision. H: p#0.28 H3: p>0.28 O.C. Ho: p#0.28 H: p= 0.28 O D. Ho: p>0.28 H: ps0.28 OF. Ho: p<0.28 H3: p= 0.28 E. Ho: p=0.28 Ha: p<0.28 What is the rejection region? Select the correct choice below and fill in the answer box(es) to complete your choice. (Round to three decimal places as needed.) O A. z< -1.645 O B. z> O C. z< or z> Calculate the value of the z-statistic for this test. (Round to two decimal places as needed.)

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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