53.2k views
4 votes
A company thinks that it might have a serious problem with its customer service arm. It is going to do a survery to estimate the population proportion that is unhappy or very unhappy with customer ser

User YuXuan Fu
by
7.8k points

1 Answer

0 votes

Final answer:

To be 90% confident that the survey's estimated proportion is within 5 percentage points of the actual population proportion of customers who click on ads on smartphones, the company should survey approximately 542 customers using a specified formula based on the desired margin of error and confidence level.

Step-by-step explanation:

Estimating a Population Proportion

To determine the number of customers a company should survey to be 90 percent confident that the estimated proportion is within 5 percentage points of the true population proportion of customers who click on ads on their smartphones, we can use the formula for sample size calculation for proportion estimates:


n = (Z² * p' * (1-p')) / E²

Where:

For a 90% confidence level, the z-score is approximately 1.645 (from z-tables). Assuming p' is 0.50 (which maximizes sample size for given E) and the margin of error (E) is 0.05, the calculation is as follows:



n = (1.645² * 0.50 * (1-0.50)) / 0.05²

n = (2.706 * 0.50 * 0.50) / 0.0025

n = 1.353 / 0.0025

n = 541.2


Therefore, the company should survey approximately 542 customers to meet the criteria.

User Elon Gated
by
8.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.