### Manual Transmission AutomobilesIn a recent year, 6% of cars sold had a manual transmission. A random sample of college students who owned cars revealed the following: out of 130 cars, 21 had manual transmissions. Estimate the proportion of college students who drive cars with manual transmissions with 99% confidence. Round intermediate and final answers to at least three decimal places.#### Calculation DetailsTo find the confidence interval, we will use the following formula for the proportion's confidence interval:\[ \hat{p} \pm Z_{\alpha/2} \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} \]- \(\hat{p}\) = Sample proportion = \(\frac{x}{n}\) - \(x\): number of manual transmission cars (21) - \(n\): total number of cars (130)- \(Z_{\alpha/2}\): Z-value for 99% confidence level (Approximately 2.576)#### Steps1. **Calculate sample proportion (\(\hat{p}\))**: \[ \hat{p} = \frac{21}{130} \]2. **Calculate the standard error (SE)**: \[ SE = \sqrt{\frac{\hat{p}(1 - \hat{p})}{130}} \]3. **Multiply the Z-value by the standard error** to find the margin of error (ME): \[ ME = Z_{\alpha/2} \times SE \]4. **Construct the confidence interval**: \[ (\hat{p} - ME, \hat{p} + ME) \]By completing these steps, we can accurately determine the requested confidence interval for the proportion of college students who drive cars with manual transmissions.#### Graphical ExplanationThere are no graphs or diagrams provided in the given image. If there were any, they would typically illustrate the normal distribution with the confidence interval marked on the bell curve, showing the central proportion and the tails representing the significant regions defined by the Z-value.This guide presents a detailed explanation of how to estimate the proportion and construct a confidence interval that can be used in instructional material on an educational website.

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Description: ### Manual Transmission AutomobilesIn a recent year, 6% of cars sold had a manual transmission. A random sample of college students who owned cars revealed the following: out of 130 cars, 21 had manual transmissions. Estimate the proportion of colle

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Manual Transmission Automobiles In a recent year, 6% of cars sold had a manual transmission. A random sample of college students who owned cars revealed the following: out of 130 cars, 21 had manual transmissions. Estimate the proportion of college students who drive cars with manual transmissions with 99% confidence. Round intermediate and final answers to at least three decimal places.

Manual Transmission Automobiles In a recent year, 6% of cars sold had a manual transmission. A random sample of college students who owned cars revealed the following: out of 130 cars, 21 had manual transmissions. Estimate the proportion of college students who drive cars with manual transmissions with 99% confidence. Round intermediate and final answers to at least three decimal places.

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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