Question

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

Answer 1

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.