Final answer:
Researchers conducting a hypothesis test to determine the proportion of Americans who own dogs will create a null and alternative hypothesis based on previous data or claims, collect sample data, and use statistical methods to test the hypotheses.
Step-by-step explanation:
When researchers are interested in estimating the proportion of Americans who own dogs, they are likely to conduct a hypothesis test. This type of test allows for making inferences about the population based on sample data. The process involves stating two hypotheses: the null hypothesis (H0) and the alternative hypothesis (H1 or Ha). The null hypothesis typically represents a status quo or a specific value that the researchers want to test against, while the alternative hypothesis represents what researchers suspect might be the case.
For instance, if previous data suggests that 40% of Americans own dogs, researchers might formulate their hypotheses as follows:
- H0: p = 0.40 (The proportion of Americans who own dogs is 40%)
- Ha: p ≠ 0.40 (The proportion of Americans who own dogs is not 40%)
After collecting and analyzing the data by using statistical methods, researchers can decide whether to reject the null hypothesis or not based on the evidence provided by the sample.