Question

A well-known hamburger chain plans on selling a new plant-based hamburger called the Implausible Burger. Suppose an employee in their marketing department is tasked with determining the proportion of potential customers who would prefer the Implausible Burger to its meat-based alternatives. Find an upper bound for the number of potential customers that the employee will have to (randomly and independently) survey to obtain an estimate at the 94% confidence level within a 1% margin of error.

Answer 1

To find an upper bound for the number of potential customers that the employee will have to survey to estimate the proportion of customers who would prefer the Implausible Burger, we can use the formula for sample size. Assuming a 94% confidence level and a 1% margin of error, the upper bound is 9604.

Step-by-step explanation:

To find an upper bound for the number of potential customers that the employee will have to survey, we need to use the formula for sample size:

[Z * (σ / E)]^2

Where Z is the z-score corresponding to the desired confidence level, σ is the standard deviation (which we don't have), and E is the desired margin of error. Since we don't have the standard deviation, we can use the conservative estimate of 0.5 for p' (the assumed proportion of potential customers who prefer the Implausible Burger) to calculate an upper bound.

Let's assume Z = 1.96 for a 94% confidence level and E = 0.01 for a 1% margin of error:

[1.96 * (0.5 / 0.01)]^2 = 9604

Therefore, an upper bound for the number of potential customers the employee will have to survey is 9604.