### Survey Analysis on Product OwnershipA random sample of 72 households was selected for a phone survey. The key question asked was, "Do you or any member of your household own a product from Company A?" Of the 72 respondents, 18 said yes and 54 said no.#### a. Determine the sample proportion, \( p \), of households that own a Company A product.- **Calculation**: The sample proportion is calculated as follows: - \( p = \frac{\text{Number of 'Yes' responses}}{\text{Total number of respondents}} = \frac{18}{72} = 0.25 \)- **Rounded Result**: \( p = 0.25 \) (rounded to two decimal places as needed).#### b. If the population proportion is 0.75, determine the standard error of the proportion.- **Formula**: The standard error of the proportion is calculated using the formula: \[ \sigma_p = \sqrt{\frac{P(1-P)}{n}} \] Where: - \( P = 0.75 \) (population proportion) - \( n = 72 \) (sample size)- **Calculation**: - \( \sigma_p = \sqrt{\frac{0.75 \times (1 - 0.75)}{72}} = \sqrt{\frac{0.75 \times 0.25}{72}} \approx 0.1636 \)- **Rounded Result**: \( \sigma_p = 0.1636 \) (rounded to four decimal places as needed).This analysis can help in understanding the market penetration of Company A's products within the surveyed population and estimate the variability expected if the entire population were surveyed.

Given Data sample size,n= 72 probability of success,p= 0.75 probability of…

Answered: A random sample of 72 households was…

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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