One Sample Hypothesis Testing Paper

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One Sample Hypothesis Testing Paper
Do Major League Baseball teams with higher salaries win more frequently than other teams? Although many people believe that the larger payroll budgets win games, which point does vary, depending on the situation. “…performances by individual players vary quite a bit from year to year, preventing owners from guaranteeing success on the field. Team spending is certainly a component in winning, but no team can buy a championship.” (Bradbury). For some, it’s hard not to root for the lower paid teams. If the big money teams, like Goliath, are always supposed to win, it’s hard not cheer for David. This paper will discuss the effects of payroll budgets on the percentage of wins for the 30 Major League Baseball teams of 2007. There’s 30 major league baseball teams divided into two divisions. The payrolls for the 2007 30 major league teams are based on a 40 man roster and include salaries and prorated shares of signing bonuses, earned incentive bonuses, non-cash compensation, buyouts of unexercised options and cash transactions. There may be some cases were parts of the salaries are deferred or discounted to reflect present-day values. The following list is in order of highest payroll. The chart on the left is payroll and the one on the right is number of wins for 2007.

Based on the charts if a team is at the top end of the payroll chances are they will have a good season, after the top eight of the payroll it’s kind of scattered. So if they want to have a strong shoot at winning you have to be in the top eight of payrolls. A team that has defied the payroll and still have just six less wins then the highest payroll and the team is Arizona who has the 23rd highest payroll and was ranked 5th in wins. Baseball teams with higher payrolls do win more games, but only to a certain point, in the case of the 2007 season it’s the top eight. 5 Step Procedure

List the Null and Alternative Hypothesis
The reach question “do baseball teams with higher payroll win more?” will for testing purposes be turned into the verbal Hypothesis statement, baseball teams with larger payrolls don’t win anymore than teams with smaller payrolls. This leads to the numerical hypothesis statements regarding the null and alternative hypotheses. Null Hypothesis: Ho=1  2

Alternative Hypothesis Ho=1 > 2
The research methodology is to divide the teams by their salary means. Then the win means will be compared to determine if there’s a significant difference in production of high salary teams and lower salary teams. 1, teams with larger payrolls, will be defined as teams with payrolls that are average or above average (see chart team A) and 2, teams with smaller payrolls, will be defined as teams with less than average payrolls (see chart team B). State the Level of Significance

Alpha:  =. 05=t.05 with 28 degrees of freedom=1.701(from Alex calculator) Test static t (because  is unknown)
Decision rule: if t>1.701 reject Ho
Calculation of test value
t=xbar1-xbar2/the square root of s squared subscript p(1/n1+1/n2) s squared subscript p=(n1-1)s squared2 subscript1+(n2-1)s squared2 subscript2]/n1+n2-2. The numerator of the function, n1+n2-2, is the degrees of freedom.

Team A (1)Team B (2)
Sample Mean85.8676.88
Sample Stdev10.659.42
Number1416
The t static = 88.86-76.88=11.98
The square root of
1474.493+1331.046/14+16-2(1/14+1/16)=
11.98the square root of 100.198(.134)=
11.983664=3.27
Decision
Since 3.27 the t statistic is in the rejection area to the right of =1.701, the level of significance, the decision is to reject the null hypothesis that teams with larger payrolls don’t win anymore than teams with smaller payroll and accept the alternative hypothesis that larger payroll team do win more. Hypothesis Test Results

The research question the researchers asked was do baseball teams with higher salaries win more baseball games. To prove this statement or hunch the 5 step...
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