Specify the competing hypotheses in order to determine wheth

Specify the competing hypotheses in order to determine whether or not the population means differ.

Solution

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    2   tailed test.      
Calculating the means of each group,              
              
X1 =    29.2          
X2 =    32.7          
              
Calculating the standard deviations of each group,              
              
s1 =    9.823441352          
s2 =    9.359487165          
              
Thus, the pooled standard deviation is given by              
              
S = sqrt[((n1 - 1)s1^2 + (n2 - 1)(s2^2))/(n1 + n2 - 2)]               
              
As n1 =    35   , n2 =    24  
              
Then              
              
S =    9.638919645          
              
Thus, the standard error of the difference is              
              
Sd = S sqrt (1/n1 + 1/n2) =    2.554551853          
Getting the critical value using table/technology,              
df = n1 + n2 - 2 =    57          

tcrit =    2.002465459          
              
Thus,as

lower bound = [X1 - X2] - tcrit S
upper bound = [X1 - X2] + tcrit S

Thus, the conifdence interval is

(-22.80, 15.80) [ANSWER, A]

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B.

H0: 1 2 = 0; HA: 1 2 0

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C.

No, since the confidence interval includes the hypothesized value of 0.