with solution too please Saimpie Poo... Saliipie pOu.. Sample Pooled Variances t

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with solution too please

Saimpie Poo... Saliipie pOu.. Sample Pooled Variances t-test Problem The tabie below comains data from the stare of Washington by type of jurisdiction wrhan versus non-urbanj abour the mumber of police officers per 1,000 residents. Use ts information to conduct a ro-tailed pooled variances i-test using an alpha level of.0S. Remember to complete all 5 steps of the ippothesis test. Sample 1: Urban Jurisdictions r, = 840 -680 si 462 Ni-13 Sample 2: Non-Urban Jurisdictions = 1.680 8-1.370 s} = 1.877 -40 Step I: State the null and alternative hypotheses *Step 2: Identify the distribution and compute the degrees of freedom Step 3: Identify the critical value of the test statistic and state the decision rule Step 4: Compute the obtained value of the test statistic. . Step 5: Make a decision about the null hypathesis and state the substantive conclusion

Explanation / Answer

Step 1:

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   =   0  
Ha:   u1 - u2   =/   0   [ANSWER]

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Step 2:

Here, we use the t distribution.

df = n1 + n2 - 2 =    51   [ANSWER]

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Step 3:      

At level of significance =    0.05          

As we can see, this is a    two   tailed test.  
Getting the critical value using table/technology,              
tcrit =    +/-   2.00758377   [ANSWER, CRITICAL VALUE]  

Hence, we reject Ho when |t| > 2.008. [ANSWER]

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STEP 4:
  
Calculating the means of each group,              
              
X1 =    0.84          
X2 =    1.68          
              
Calculating the standard deviations of each group,              
              
s1 =    0.68          
s2 =    1.37          
              
Thus, the pooled standard deviation is given by              
              
S = sqrt[((n1 - 1)s1^2 + (n2 - 1)(s2^2))/(n1 + n2 - 2)]               
              
As n1 =    13   , n2 =    40  
              
Then              
              
S =    1.242608736          
              
Thus, the standard error of the difference is              
              
Sd = S sqrt (1/n1 + 1/n2) =    0.396707732          
              
As ud = the hypothesized difference between means =    0   , then      
              
t = [X1 - X2 - ud]/Sd =    -2.117427848   [ANSWER, TEST STATISTIC]

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As |t| > 2.008, we   REJECT THE NULL HYPOTHESIS.  

Hence, there is significant differnce between the mean number of police officers per 1000 residents in Urban and Non-urban jurisdictions. [CONCLUSION]      

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Hi! If you use another method/formula in calculating the degrees of freedom in this t-test, please resubmit this question together with the formula/method you use in determining the degrees of freedom. That way we can continue helping you! Thanks!

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