A recent study of 100 social workers in a southern state found that their mean salary was $23,000 with a standard deviation of $2100. A similar study of 95 social workers in a western state found that their mean salary was $34,200 with a standard deviation of$3200.   Find the test statistic and critical value when the claim that the mean salaries of social workers in the western state is greater than that of social workers in the southern state. Use α = 0.05. Sample1:  Social workers in a southern state,  Sample2:  Social workers in awestern state. a) Find the test statistic  b) Find critical value

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A recent study of 100 social workers in a southern state found that their mean salary was $23,000 with a standard deviation of $2100. A similar study of 95 social workers in a western state found that their mean salary was $34,200 with a standard deviation of$3200.   Find the test statistic and critical value when the claim that the mean salaries of social workers in the western state is greater than that of social workers in the southern state. Use α = 0.05.

Sample1:  Social workers in a southern state,  Sample2:  Social workers in awestern state.

a) Find the test statistic 

b) Find critical value

Expert Solution
Step 1

a). Sample1-

sample size=n1=100

sample mean=$23000=x1

population mean=μ1

s1=$2100

Sample2-

sample size=n2=95

sample mean=x2=$34200

population mean=μ2

s2=$3200

hypotheses to be tested here will be,

H0:μ1=μ2 vs H2:μ1<μ2

So, the test statistic will be given by,

t=x1-x2-μ1-μ2s1n1+1n2

where 

s2=n1-1s12+n2-1s22n1+n2-2    =7249481.865

Therefore, s=2692.486

Value of t under null hypothesis is -29.029

So, t=29.029

 

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