A random sample of 11 observations from one population revealed a sample mean of

Question

A random sample of 11 observations from one population revealed a sample mean of 24 and a sample deviation of 5. A random sample of 5 observations from another population revealed a sample mean of 25 and a sample standard deviation of 3.5.

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 11 observations from one population revealed a sample mean of 24 and a sample deviation of 5. A random sample of 5 observations from another population revealed a sample mean of 25 and a sample standard deviation of 3.5.

Explanation / Answer

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   =   0  
Ha:   u1 - u2   =/   0  
At level of significance =    0.1          
As we can see, this is a    two   tailed test.  
Here,

n1 = sample size of group 1 =    11          
n2 = sample size of group 2 =    5          
Thus, df = n1 + n2 - 2 =    14          

Now, the critical value for t is              
              
tcrit =    +/-   1.761

Hence, reject Ho when t < -1.761 or t > 1.761. [ANSWER]

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b)

Calculating the standard deviations of each group,              
              
s1 =    5          
s2 =    3.5          
              
Thus, the pooled standard deviation is given by              
              
S = sqrt[((n1 - 1)s1^2 + (n2 - 1)(s2^2))/(n1 + n2 - 2)]               
              
As n1 =    11   , n2 =    5  
              
Then              
              
S =    4.621378891          

Hence, the pooled variance is

S^2 = 4.621378891^2 = 21.35714285 [ANSWER]

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c)

Calculating the means of each group,              
              
X1 =    24          
X2 =    25          
              
              
Thus, the standard error of the difference is              
              
Sd = S sqrt (1/n1 + 1/n2) =    2.49258641          
              
As ud = the hypothesized difference between means =    0   , then      
              
t = [X1 - X2 - ud]/Sd =    -0.401189702   [ANSWER, TEST STATISTIC]

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d)

As |t| < 1.761, we   DO NOT REJECT THE NULL HYPOTHESIS.   [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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