Final Answer:
The correct hypothesis statements for this test are:
[ H_0: mu_a = mu_n ]
[ H_a: mu_a neq mu_n ]
Step-by-step explanation:
In the context of this hypothesis test, ( mu_a ) represents the population mean salary of players in the American League, and ( mu_n ) represents the population mean salary of players in the National League. The null hypothesis ( H_0 assumes that there is no difference in the mean salary between the two leagues (( mu_a = mu_n )), while the alternative hypothesis ( H_a ) suggests that there is a significant difference in mean salary between the American and National Leagues (( mu_a neq mu_n )).
To perform this hypothesis test, one would typically use a t-test, as mentioned in the question. The t-test assesses whether the means of two groups are statistically different from each other, taking into account the variability within each group.
The significance level of 0.05 indicates that if the probability of observing the data given that the null hypothesis is true is less than 0.05, then the null hypothesis can be rejected. The test statistic and critical values would be calculated based on the sample data, and then compared to the critical region to make a decision about rejecting or failing to reject the null hypothesis.
It's important to note that the actual test statistic calculation and critical region comparison would involve more detailed statistical calculations based on the provided data, which can be performed using statistical software or tools.