The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition. He wants to first determine the percentage of adults who have heard of the brand. How many adults must he survey in order to be 80% confident that his estimate is within seven percentage points of the true population percentage? Complete parts (a) through (c) below. a) Assume that nothing is known about the percentage of adults who have heard of the brand. n= (Round up to the nearest integer.) b) Assume that a recent survey suggests that about 87% of adults have heard of the brand. n3= (Round up to the nearest integer.) c) Given that the required sample size is relatively smalI, could he simply survey the adults at the nearest college? O A. No, a sample of students at the nearest college is a stratified sample, not a simple random sample, so it is very possible that the results would not be representative of the population of adults. O B. No, a sample of students at the nearest college is a cluster sample, not a simple random sample, so it is very possible that the results would not be representative of the population of adults. O C. Yes, a sample of students at the nearest college is a simple random sample, so the results should be representative of the population of adults. O D. No, a sample of students at the nearest college is a convenience sample, not a simple random sample, so it is very possible that the results would not be representative of the population of adults. Click to select your answer(s). MacBook DI DD 80 888 F10 F11 F12 esc F7 F8 F9 F1 F2 F3 F4 F5 F6 @ # $ %3D 4 6 7 8. { T Y U 0 P R + & LO

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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Transcribed Image Text:**Title: Determining Sample Size for Brand Recognition Campaign** The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition. To do this, he needs to first determine the percentage of adults who have heard of the brand. The goal is to be 80% confident that the estimate is within seven percentage points of the actual population percentage. The process includes solving the following: ### Steps to Determine Sample Size: 1. **Assuming Nothing is Known About Brand Awareness:** - Calculate the required sample size assuming no prior knowledge about the percentage of adults who have heard of the brand. - **n =** *(Round up to the nearest integer.)* 2. **Using Recent Survey Data:** - Given that a recent survey suggests that about 87% of adults have heard of the brand. - **n =** *(Round up to the nearest integer.)* 3. **Evaluating Sampling Methods:** - Considering that the required sample size is relatively small, determine if surveying the adults at the nearest college is a valid approach. - Evaluate the type of sample and whether it would be representative of the population of adults. ### Question: **Given that surveying the nearest college students is being considered, choose the correct option regarding sampling:** - **A.** No, a sample of students at the nearest college is a stratified sample, not a simple random sample, so it is very possible that the results would not be representative of the population of adults. - **B.** No, a sample of students at the nearest college is a cluster sample, not a simple random sample, so it is very possible that the results would not be representative of the population of adults. - **C.** Yes, a sample of students at the nearest college is a simple random sample, so the results should be representative of the population of adults. - **D.** No, a sample of students at the nearest college is a convenience sample, not a simple random sample, so it is very possible that the results would not be representative of the population of adults. Click to select your answer(s). --- *Note: There are no specific graphs or diagrams in the original content provided.*

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