Question

At a local store, 65 female employees were randomly selected and it was found that their mean monthly income was $625 with a standard deviation of $121.50. Seventy-five male employees were also randomly selected and their mean monthly income was found to be $667 with a standard deviation of $168.70. Test the hypothesis that male employees have a higher monthly income than female employees. Use α = 0.01. Use any method, however, follow the PHANTOMS acronym.

P - Parameter Statement

H - Hypotheses

A - Assumptions & Conditions

N - Name the Test and state the curve you're using

T - Test Statistic - Round your value to TWO decimals and state the command you used to find this value

O - Obtain the

P-Value or Critical Value . State the command you are using to find these values

M - Make a Decision about the Null Hypothesis and explain why

S - State Your Conclusion About the Claim

Answer 1

P

male employees have a higher monthly income than female employees

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H

Ho :   µ1 - µ2 =   0
Ha :   µ1-µ2 <   0
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A=

population from which samples are taken are normally distributed

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N=

Hypothesis test: Difference of two means (two independnet sample t test)

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T=

Sample #1   ---->   1                  
mean of sample 1,    x̅1=   625.000                  
standard deviation of sample 1,   s1 =    121.500                  
size of sample 1,    n1=   65                  
                          
Sample #2   ---->   2                  
mean of sample 2,    x̅2=   667.000                  
standard deviation of sample 2,   s2 =    168.700                  
size of sample 2,    n2=   75                  
                          
difference in sample means =    x̅1-x̅2 =    625.0000   -   667.0   =   -42.00  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    148.6851                  
std error , SE =    Sp*√(1/n1+1/n2) =    25.1967                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   -42.0000   -   0   ) /    25.20   =   -1.67

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O=

  

Degree of freedom, DF=   n1+n2-2 =    138  
t-critical value , t* =        -2.354   (excel function: =t.inv(α,df)

p-value =        0.048903   [ excel function: =T.DIST(t stat,df) ]

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M=

p-value>α , Do not reject null hypothesis  
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S

There is not enough evidence to conclude that  male employees have a higher monthly income than female employees.