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In: Statistics and Probability

The income of males in each state of the United States, including the District of Columbia...

The income of males in each state of the United States, including the District of Columbia and Puerto Rico, are given in table #9.3.3, and the income of females is given in table #9.3.4 ("Median income of," 2013). Is there enough evidence to show that the mean income of males is more than of females? Test at the 1% level.

Table #9.3.3: Data of Income for Males

$42,951

$52,379

$42,544

$37,488

$49,281

$50,987

$60,705

$50,411

$66,760

$40,951

$43,902

$45,494

$41,528

$50,746

$45,183

$43,624

$43,993

$41,612

$46,313

$43,944

$56,708

$60,264

$50,053

$50,580

$40,202

$43,146

$41,635

$42,182

$41,803

$53,033

$60,568

$41,037

$50,388

$41,950

$44,660

$46,176

$41,420

$45,976

$47,956

$22,529

$48,842

$41,464

$40,285

$41,309

$43,160

$47,573

$44,057

$52,805

$53,046

$42,125

$46,214

$51,630

Table #9.3.4: Data of Income for Females

$31,862

$40,550

$36,048

$30,752

$41,817

$40,236

$47,476

$40,500

$60,332

$33,823

$35,438

$37,242

$31,238

$39,150

$34,023

$33,745

$33,269

$32,684

$31,844

$34,599

$48,748

$46,185

$36,931

$40,416

$29,548

$33,865

$31,067

$33,424

$35,484

$41,021

$47,155

$32,316

$42,113

$33,459

$32,462

$35,746

$31,274

$36,027

$37,089

$22,117

$41,412

$31,330

$31,329

$33,184

$35,301

$32,843

$38,177

$40,969

$40,993

$29,688

$35,890

$34,381

Solutions

Expert Solution

Ho :   µ1 - µ2 =   0          
Ha :   µ1-µ2 >   0          
                  
Level of Significance ,    α =    0.01          
                  
Sample #1   ----> male   
mean of sample 1,    x̅1=   46453.31          
standard deviation of sample 1,   s1 =    7030.712514          
size of sample 1,    n1=   52          
                  
Sample #2   ---->   female   
mean of sample 2,    x̅2=   36511.000          
standard deviation of sample 2,   s2 =    6138.12          
size of sample 2,    n2=   52          
                  
difference in sample means = x̅1-x̅2 =    46453.308   -   36511.0000   =   9942.3077
                  
std error , SE =    √(s1²/n1+s2²/n2) =    1294.2733          


t-statistic = ((x̅1-x̅2)-µd)/SE = (   9942.3077   /   1294.2733   ) =   7.6818


                  
Degree of freedom, =   100          
                  
p-value =        0.0000   [excel function: =T.DIST.RT(t stat,df) ]  

  
Conclusion:     p-value<α , Reject null hypothesis          

  
there is enough evidence that  mean income of males is more than of females

orchestra answered 1 year ago
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