The null hypothesis (H0) suggests no change or no decrease in the preference for baseball among Americans under 40, while the alternative hypothesis (Ha) claims a lower preference for baseball in this age group.
In hypothesis testing, we set up a null hypothesis (H0) and an alternative hypothesis (Ha). The null hypothesis typically represents a statement of no effect or no difference, while the alternative hypothesis asserts a claim or suggests a difference.
In this scenario, where we are testing the claim that the percentage of Americans younger than 40 years old who identify baseball as their favorite sport is lower than 9%, the hypotheses can be set up as follows:
H0: p is greater than or equal to 0.09
Ha: p is less than 0.09
Here, p represents the true proportion of Americans younger than 40 years old who identify baseball as their favorite sport.
The null hypothesis (H0) states that the true proportion is greater than or equal to 9%, indicating that there is no evidence to suggest a lower preference for baseball among Americans under 40.
On the other hand, the alternative hypothesis (Ha) asserts that the true proportion (p) is less than 9%, supporting the claim that the percentage is lower among Americans younger than 40 years old.
In summary:
H0: p is greater than or equal to 0.09
Ha: p is less than 0.09