Sample Size Calculation for Population Proportion

This lesson explains how to calculate the sample size needed for a population proportion given a specific margin of error. It introduces the error bound formula and demonstrates its application through an example involving a mobile phone company surveying customers. The lesson covers finding the z-score for a confidence level, determining sample proportions, and maximizing the product of these proportions to ensure a large enough sample size. The final calculation is performed, emphasizing the importance of rounding up to meet the requirements.

What is the purpose of using the error bound formula in sample size calculation?

• To determine the exact population size

• To calculate the required sample size for a desired margin of error

• To estimate the total number of customers

• To find the average age of a population

In the example scenario, what is the age group of customers the mobile phone company is interested in?

• Customers aged 50+

• Customers aged 30+

• Customers aged 40+

• Customers aged 60+

What is the main goal of the mobile phone company's survey?

• To calculate the average age of customers

• To estimate the total revenue from customers

• To determine the percentage of customers aged 50+ using text messaging

• To find the total number of customers

What confidence level is used in the example to determine the sample size?

• 80%

• 95%

• 85%

• 90%

Why is it important to find the z-score corresponding to the confidence level?

• To calculate the average error

• To determine the sample size

• To estimate the total population

• To find the population mean

What is the error bound expressed as a decimal in the example?

• 0.01

• 0.03

• 0.02

• 0.04

What is the z-score for a 90% confidence level?

• 2.58

• 1.96

• 1.645

• 2.33

What values of p-prime and q-prime are used to maximize the product in the sample size formula?

• 0.4 and 0.6

• 0.6 and 0.4

• 0.3 and 0.7

• 0.5 and 0.5

Why is it necessary to round up the calculated sample size?

• To match the population size

• To reduce the margin of error

• To make calculations easier

• To ensure the sample size is large enough

What is the calculated sample size needed for the mobile phone company to achieve the desired confidence level and margin of error?

• 850

• 800

• 700

• 752