The company offers two types of sales: 1. Internet sales; 2. Store sales. The marketing research manager believes that the Internet sales are more than 10% higher than store sales. The null hypothesis would be:
A. Pinternet–Pstore >.10
B. Pinternet–Pstore <.10
C. Pinternet–Pstore less than or equal to .10
D. Pinternet–Pstore greater than or equal to.10
E. Pinternet–Pstore less than or equal to 0
To determine the null hypothesis in this scenario, we need to first understand the concept of null hypothesis and the specific statement being made about the sales.
The null hypothesis (H₀) is a statement that assumes there is no significant difference or relationship between variables. It is the default assumption unless there is substantial evidence to support an alternative hypothesis (H₁).
In this case, the marketing research manager believes that the Internet sales are more than 10% higher than store sales. To represent this statement in terms of proportions, we can use the following formula:
Pinternet - Pstore > 0.10,
where Pinternet represents the proportion of Internet sales and Pstore represents the proportion of store sales.
Looking at the answer choices, we can see that option C. Pinternet–Pstore less than or equal to .10 correctly represents the null hypothesis. This option assumes that the difference between the two proportions (Internet sales and store sales) is less than or equal to 0.10, meaning it allows for the possibility that the Internet sales may not be more than 10% higher than store sales.
Therefore, the correct answer is option C. Pinternet–Pstore less than or equal to .10.