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A large collection of one-digit random numbers should have about 50% odd and 50% even digits because five of the ten digits are odd (1, 3, 5, 7, and 9) and five are even (0, 2, 4, 6, and 8). a. Find the proportion of odd-numbered digits in the following lines from a random number table. Count carefully. 90963 19 277 12708 58589 5 4 6 4 1 89392 b. Does the proportion found in part (a) represent p (the sample proportion) or p (the population proportion)? c. Find the error in this estimate, the difference between p and p (or p-p). ... a. The given random number table consists of % odd-numbered digits. (Round to two decimal places as needed.)

A large collection of one-digit random numbers should have about 50% odd and 50% even digits because five of the ten digits are odd (1, 3, 5, 7, and 9) and five are even (0, 2, 4, 6, and 8). a. Find the proportion of odd-numbered digits in the following lines from a random number table. Count carefully. 90963 19 277 12708 58589 5 4 6 4 1 89392 b. Does the proportion found in part (a) represent p (the sample proportion) or p (the population proportion)? c. Find the error in this estimate, the difference between p and p (or p-p). ... a. The given random number table consists of % odd-numbered digits. (Round to two decimal places as needed.)

MATLAB: An Introduction with Applications
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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--- **Understanding Proportions and Random Numbers** **Concept Overview:** A large collection of one-digit random numbers should have about 50% odd and 50% even digits because five of the ten digits are odd (1, 3, 5, 7, and 9) and five are even (0, 2, 4, 6, and 8). **Exercises:** a. **Find the Proportion of Odd-Numbered Digits** Examine the following lines of random numbers and count the odd digits: ``` 90963 19277 12708 58589 54641 89392 ``` **Step-by-Step Solution:** 1. Identify and count the odd digits in the given random number table: - First line: \( 9, 9, 9, 3, 1, 9, 2, 7, 7, 1, 1, 7 \) (8 odd digits) - Second line: \( 5, 5, 5, 9, 5, 7, 5, 3, 1, 3, 9 \) (9 odd digits) 2. Calculate the total number of digits: \(15 + 15 = 30\) 3. Calculate the proportion of odd digits: \[ \text{Proportion} = \frac{\text{Total Number of Odd Digits}}{\text{Total Number of Digits}} = \frac{17}{30} \approx 0.57 \] b. **Understanding Proportions:** - The proportion found in part (a) represents \(\hat{p}\) (the sample proportion) since it was calculated based on a sample of random digits. \(\hat{p}\) is an estimate of the population proportion \(p\). c. **Finding the Estimation Error:** - The error in this estimate is the difference between \(\hat{p}\) (sample proportion) and \(p\) (population proportion): \[ \text{Error} = \hat{p} - p = 0.57 - 0.50 = 0.07 \] --- **Additional Calculation Verification:** In question (a): - After recounting, the proportion of odd-numbered digits in decimal form is \(
Transcribed Image Text:--- **Understanding Proportions and Random Numbers** **Concept Overview:** A large collection of one-digit random numbers should have about 50% odd and 50% even digits because five of the ten digits are odd (1, 3, 5, 7, and 9) and five are even (0, 2, 4, 6, and 8). **Exercises:** a. **Find the Proportion of Odd-Numbered Digits** Examine the following lines of random numbers and count the odd digits: ``` 90963 19277 12708 58589 54641 89392 ``` **Step-by-Step Solution:** 1. Identify and count the odd digits in the given random number table: - First line: \( 9, 9, 9, 3, 1, 9, 2, 7, 7, 1, 1, 7 \) (8 odd digits) - Second line: \( 5, 5, 5, 9, 5, 7, 5, 3, 1, 3, 9 \) (9 odd digits) 2. Calculate the total number of digits: \(15 + 15 = 30\) 3. Calculate the proportion of odd digits: \[ \text{Proportion} = \frac{\text{Total Number of Odd Digits}}{\text{Total Number of Digits}} = \frac{17}{30} \approx 0.57 \] b. **Understanding Proportions:** - The proportion found in part (a) represents \(\hat{p}\) (the sample proportion) since it was calculated based on a sample of random digits. \(\hat{p}\) is an estimate of the population proportion \(p\). c. **Finding the Estimation Error:** - The error in this estimate is the difference between \(\hat{p}\) (sample proportion) and \(p\) (population proportion): \[ \text{Error} = \hat{p} - p = 0.57 - 0.50 = 0.07 \] --- **Additional Calculation Verification:** In question (a): - After recounting, the proportion of odd-numbered digits in decimal form is \(
### Understanding Proportions in Random Number Tables A large collection of one-digit random numbers should have about 50% odd and 50% even digits because five of the ten digits are odd (1, 3, 5, 7, and 9) and five are even (0, 2, 4, 6, and 8). **Exercise:** 1. **Find the Proportion of Odd-Numbered Digits:** Calculate the proportion of odd-numbered digits in the following lines from a random number table. Count carefully. ``` 9 0 9 6 3 1 9 2 7 7 1 2 7 0 8 5 8 5 8 5 4 6 4 1 8 9 3 9 2 ``` 2. **Interpret Proportion:** Determine if the proportion found in part (a) represents \( \hat{p} \) (the sample proportion) or \( p \) (the population proportion). 3. **Calculate Error in Estimate:** Find the error in the estimate, which is the difference between \( p \) and \( \hat{p} \) (or \( \hat{p} - p \)). ### Solution: **a. Calculation of Odd-Numbered Digit Proportion:** Let's manually count the number of odd and even digits in the given random numbers: - Row 1: 9 0 9 6 3 1 9 2 7 7 1 2 7 0 8 - Odd Digits: 9, 9, 3, 1, 9, 7, 7, 1, 7 (Total: 9) - Even Digits: 0, 6, 2, 2, 0, 8 (Total: 6) - Row 2: 5 8 5 8 5 4 6 4 1 8 9 3 9 2 - Odd Digits: 5, 5, 5, 1, 9, 3, 9 (Total: 7) - Even Digits: 8, 8, 4, 6,
Transcribed Image Text:### Understanding Proportions in Random Number Tables A large collection of one-digit random numbers should have about 50% odd and 50% even digits because five of the ten digits are odd (1, 3, 5, 7, and 9) and five are even (0, 2, 4, 6, and 8). **Exercise:** 1. **Find the Proportion of Odd-Numbered Digits:** Calculate the proportion of odd-numbered digits in the following lines from a random number table. Count carefully. ``` 9 0 9 6 3 1 9 2 7 7 1 2 7 0 8 5 8 5 8 5 4 6 4 1 8 9 3 9 2 ``` 2. **Interpret Proportion:** Determine if the proportion found in part (a) represents \( \hat{p} \) (the sample proportion) or \( p \) (the population proportion). 3. **Calculate Error in Estimate:** Find the error in the estimate, which is the difference between \( p \) and \( \hat{p} \) (or \( \hat{p} - p \)). ### Solution: **a. Calculation of Odd-Numbered Digit Proportion:** Let's manually count the number of odd and even digits in the given random numbers: - Row 1: 9 0 9 6 3 1 9 2 7 7 1 2 7 0 8 - Odd Digits: 9, 9, 3, 1, 9, 7, 7, 1, 7 (Total: 9) - Even Digits: 0, 6, 2, 2, 0, 8 (Total: 6) - Row 2: 5 8 5 8 5 4 6 4 1 8 9 3 9 2 - Odd Digits: 5, 5, 5, 1, 9, 3, 9 (Total: 7) - Even Digits: 8, 8, 4, 6,
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