Question

RTandom sample of 33 professional baseball salaries from 1985 through 2015 was seleoted. The league of the player (American or National) recorded. Salary (in thousands of dollars) and league are shown in the accompanying table. Test the hypothesis that there is a difference in th salary of players in each league. Assume the distributions are Normal enough to use the f-test. Use a significance level of 0. . O5. Fi7 Click the icon to view the data table. Determine the hypotheses for this test. Let μa​ be the population mean salary of players in the Amencan League and let μn​ be the population mez salary of players in the National League Choose the correot answer below Data Table A random sample of 33 professional baseball salanes from 1985 through 2015 was selected. The league of the player (Amencan or Nationai) was als recorded. Salary (in thousands of dollars) and league are shown in the accompanying table. Test the hypothesis that there is a difference in the mear satary of players in each league. Assume the distrbutions are Norma enough to use the t-test Use a significance level of 0.05. Click the icon to view the data table. Determine the hypotheses for this test. Lot μa​ be the population mean salary of players in the Amencan League and let μn​ be the population mean salary of players in the National League Choose the correct answer below. A. H0​:μ3​/μ0​ Ha​/μa​μi​μh​ b. H0​⋅μ3​/μ0​ Ha​μa​=μn​ Find the test statisted for this tebt.

Answer 1

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.

Answer 2

The null hypothesis (H₀) and alternative hypothesis (H₂) for this test are:

H₀: μₐ = μₙ

Hₐ: μₐ ≠ μₙ

where:

μₐ is the population mean salary of players in the American League.

μₙ is the population mean salary of players in the National League.

Step-by-step explanation:

The research question is whether there is a difference in the mean salaries of players in the American and National leagues. The null hypothesis assumes that there is no difference, meaning the mean salaries are equal (μₐ = μₙ). The alternative hypothesis states the opposite, that there is a difference in the mean salaries (μₐ ≠ μₙ).

This is a two-tailed test because we are interested in whether the mean salaries differ in any direction, not just if one is higher or lower than the other.

The provided information about the sample size, significance level, and normality assumption are relevant for calculating the test statistic and interpreting the results, but they do not affect the formulation of the hypotheses themselves.