Below I need this problem solved please let me know if you ...
Below I need this problem solved please let me know if you need any other information:
Problem Statement: Who gets paid more, teams in the National League or teams in the American League?
Hypothesis:
H0: The National league and American league teams get paid the same.
H0: μ1 = μ2
H1: The American league teams are higher paid than the National league teams.
H1: μ1 < μ2
H2: The National league teams are higher paid than the American league teams.
H2: μ1 > μ2
I will attach another link for the 2005 baseball statistics. I need this hypothesis solved with a 95% confidence interval, at a 0.05 level of significance.
Assumptions:
The two populations we are comparing are average team salaries (in millions) between the National League and American League. We are not given that the salaries from each league normally distributed. (Let me know if you need a formal assessment of normality.) We must assume that the samples were randomly selected and should therefore be independent. We do not know the two population standard deviations [pic]and [pic] so we must use the t test. (Let me know if we must first use the [pic]test value for comparing two population standard deviations [pic]and [pic] to determine whether we should pool or not pool variances.)
Using the P-value Method
1. We are testing if a difference exists between the mean team salaries of baseball teams from the National and American leagues. Let population 1 be National League Teams, and population 2 be American League Teams. The correct hypothesis is,
Hypothesis:
H0: The National league and American league teams get paid the same.
H0: μ1 = μ2 or μ1 - μ2 = 0
H1: The American league teams are higher paid than the National league teams.
H1: μ1 < μ2
H2: The National league teams are higher paid than the American league teams.
H2: μ1 > μ2
This is a two-tailed test.
2. The formula for a [pic] Confidence Interval for the difference between two Population Means [pic] for small independent samples with unequal variances is:
[pic]
|National League |American League |
|[pic]= $70.95 million |[pic] = $75.48 million |
|[pic] = $20.67 million |[pic] = $45.93 million |
|[pic] = 16 |[pic] = 14 |
The [pic]value with 95% confidence can be found by finding the value [pic]with an area of 0.025 to the left using a t distribution with degrees of freedom = [pic]. [pic]= 2.0484
Subbing the values into the confidence interval formula:
[pic]
[pic]
[pic]
So, a 95% confidence interval estimate for the mean difference between the average salaries of the National and American leagues is (-$32.57 million , $23.50 million).
3. Because the value of 0 (no difference between salaries) is in this interval, we Do Not Reject [pic].
4. Because we Do Not Reject [pic], there does not appear to be a significant difference between the mean salaries of National League Teams and American League Teams.
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