Final answer:
On a perceptual map, zero percent of customers would be interested in a product positioned outside of the rough cuts. Option A
Step-by-step explanation:
On a perceptual map, products are positioned according to how they are perceived by customers in contrast to competing products. When a product is positioned outside of the rough cuts (which are the basic criteria that customers use to consider a product as a viable option), theoretically, the percentage of customers interested in that product should be zero percent (A).
This is because the product falls outside of the minimum requirements that customers are looking for, making it very unlikely for customers to consider purchasing it.
Regarding the hypothesis test question, if we are evaluating the proportion of respondents that prefer Brand A, we should utilize a distribution that is suitable for proportion data.
In this case, the binomial distribution would be the appropriate choice since we are dealing with yes/no or success/failure outcomes, but more commonly the normal distribution is used for proportion hypothesis tests when the sample size is large enough due to the central limit theorem.
This involves checking if the observed proportion (39 percent in this case) is significantly different from the expected proportion (42 percent).
Focusing on the question about the internet marketing company, they are seeking to achieve a certain level of confidence in their estimate of the proportion of customers that click on ads on their smartphones.
To determine the sample size needed for this estimate with a 90 percent confidence level and a margin of error within ±5 percentage points, the company could use a sample size calculation formula designed for proportions.
Assuming they do not have a prior estimate, they could use the most conservative proportion, which is p' = 0.50. This maximizes the required sample size and ensures the margin of error does not exceed 5 percentage points for the estimate. Option A