Question

(Table: Baseball Salaries) Does the average salary of third basemen differ from that of shortstops? Five third basemen and five shortstops were selected at random from the National League. Their 2005 season salaries (in millions of dollars) appear in the table. Perform all six steps of the appropriate hypothesis test on this set of data.

Table: Baseball Salaries

Third Baseman	Shortstop
1.300	0.316
0.316	0.322
3.000	3.850
0.525	0.700
0.425	4.600

Step 1: What are the populations?

Step 2: State the Null hypothesis:  

Research hypothesis:  

Step 3: The comparison distribution is a _____________ distribution? (z, t or F)

Show the numbers/work:

X	X – M	(X – M)2	Y	Y – M	(Y – M)2
M = SD =			M = SD =

      

s² x =     

s²y =   

df_x =      

df_y =      

df_total =      

s²_pooled =      

s²_MX =      

s²_MY =        

s²_difference =      

s _difference =      

Step 4:

What are the critical values?  

Step 5:

t =      

=t

Step 6:

Reject or Fail to Reject       

Answer 1

Let be the population mean

Null hypothesis

Or in words Null hypothesis is H₀: the average salary of third basemen does not differ from that of shortstops

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The comparison distribution is a _______t______ distribution

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sample mean of x=

sample standard deviation of x=sx= 1.124  

sample mean of y=

sample standard deviation of y=sy=2.093

s2x=1.124  ²= 1.263

s2y=2.093²= 4.379

dfx=5-1=4

dfy=5-1=4

dftotal=4+4=8

s2pooled =

s2MX = 0.5

s2MY=0.94

s2 differernce =-3.116

s difference=-0.969

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crittical values=

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t=

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As t>-t_0.025;8 and t<t_0.025;8

Fail to Reject H0

And conclude that the average salary of third basemen does not differ from that of shortstops

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