Question

You wish to test the following claim (H) at a significance level of a = 0.001. H:M1 = H2 H:41 € M2 You obtain a sample of size n1 = 101 with a mean of M = 79.4 and a standard deviation of SD = 15.3 from the first population. You obtain a sample of size ny = 36 with a mean of M2 and a standard deviation of SD2 = 14.4 from the second population. What is the critical value for this test? (Report answer accurate to three decimal places.) critical value + 80.8 What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic - -0.4925877 The test statistic is... O in the critical region O not in the critical region This test statistic leads to a decision to... O reject the nult O accept the null O fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the first population mean is not equal to the second population mean. There is not sufficient evidence to warrant rejection of the claim that the first population mean is not equal to the second population mean. O The sample data support the claim that the first population mean is not equal to the second population mean.

Answer 1

Ho :   µ1 - µ2 =   0
Ha :   µ1-µ2 ╪   0
      
Level of Significance ,    α =    0.001
Degree of freedom, DF=   n1+n2-2 =    135
t-critical value , t* = -3.364 , 3.364

..............

Sample #1   ---->   1                  
mean of sample 1,    x̅1=   79.400                  
standard deviation of sample 1,   s1 =    15.300                  
size of sample 1,    n1=   101                  
                          
Sample #2   ---->   2                  
mean of sample 2,    x̅2=   80.800                  
standard deviation of sample 2,   s2 =    14.400                  
size of sample 2,    n2=   36                  
                          
difference in sample means =    x̅1-x̅2 =    79.4000   -   80.8   =   -1.40  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    15.0718                  
std error , SE =    Sp*√(1/n1+1/n2) =    2.9256                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   -1.4000   -   0   ) /    2.93   =   -0.479

..............

O not in the critical region

O fail to reject the null

mean. There is not sufficient evidence to warrant rejection of the claim that the first population mean is not equal to the second population mean.

...............

Please let me know in case of any doubt.

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