In the testing, whether the means of two normal populations are equal, summary s

Question

In the testing, whether the means of two normal populations are equal, summary statistics computed for two independent samples are as follows

N2 = 35

S2 = 1.20

assume that the population variances are equal. What is the value of the Test statistic you would use to test the claim that the two means are not equal?

a) 1.607 b) 1.611 c) 1.553 d) 1.319

For test statistic formula, should i use the one with pooled variance (S2p) or not?

N2 = 35

S2 = 1.20

Explanation / Answer

Data:        

n1 = 20       

n2 = 35       

x1-bar = 7.3       

x2-bar = 6.8       

s1 = 1.05       

s2 = 1.2       

Hypotheses:        

Ho: 1 = 2        

Ha: 1 2        

Decision Rule:        

= 0.05       

Degrees of freedom = 20 + 35 - 2 = 53      

Lower Critical t- score = -2.005745949       

Upper Critical t- score = 2.005745949       

Reject Ho if |t| > 2.005745949       

Test Statistic:        

Pooled SD, s = [{(n1 - 1) s1^2 + (n2 - 1) s2^2} / (n1 + n2 - 2)] =   (((20 - 1) * 1.05^2 + (35 - 1) * 1.2^2)/(20 + 35 -2)) =     1.148

SE = s * {(1 /n1) + (1 /n2)} = 1.14848135986714 * ((1/20) + (1/35)) = 0.321926165      

t = (x1-bar -x2-bar)/SE = 1.553151172    

Option C.   

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