A random sample of 8 observations from one population revealed a sample mean of

Question

A random sample of 8 observations from one population revealed a sample mean of 23 and a sample deviation of 3.9. A random sample of 8 observations from another population revealed a sample mean of 28 and a sample standard deviation of 4.4.

State the decision rule. (Negative values should be indicated by a minus sign. Round your answer to 3 decimal places.)

Compute the test statistic.(Negative value should be indicated by a minus sign.Round your answer to 3 decimal places.)

A random sample of 8 observations from one population revealed a sample mean of 23 and a sample deviation of 3.9. A random sample of 8 observations from another population revealed a sample mean of 28 and a sample standard deviation of 4.4.

Explanation / Answer

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   =   0  
Ha:   u1 - u2   =/   0  
At level of significance =    0.05          
As we can see, this is a    two   tailed test.  
Getting the critical value using table/technology,              
df = n1 + n2 - 2 =    14          

tcrit =    +/-   2.144786688

Hence, reject Ho if t < -2.145 or t > 2.145. [CONCLUSION]

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b)      

Calculating the standard deviations of each group,              
              
s1 =    3.9          
s2 =    4.4          
              
Thus, the pooled standard deviation is given by              
              
S = sqrt[((n1 - 1)s1^2 + (n2 - 1)(s2^2))/(n1 + n2 - 2)]               
              
As n1 =    8   , n2 =    8  
              
Then              
              
S =    4.157523301          

Hence,

S^2 = 17.285 [ANSWER, POOLED VARIANCE]

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c)
  
Calculating the means of each group,              
              
X1 =    23          
X2 =    28          
              
              
Thus, the standard error of the difference is              
              
Sd = S sqrt (1/n1 + 1/n2) =    2.078761651          
              
As ud = the hypothesized difference between means =    0   , then      
              
t = [X1 - X2 - ud]/Sd =    -2.405278161   [ANSWER, TEST STATISTIC]

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d)      
              
              
As t < -2.145, we reject Ho. [ANSWER]

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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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