This data is heights for 50 men and 50 women. You want to know if the genders di

Question

This data is heights for 50 men and 50 women. You want to know if the genders differ in height. What test do you use? Perform the test and present your results. HEIGHT (inches) Women Men 60 62 72 67 59 65 62 69 63 72 61 75 72 77 69 68 67 70 68 71 71 74 57 69 59 67 61 72 65 73 63 71 68 71 66 70 66 70 67 63 64 67 62 69 61 73 66 70 65 70 69 69 72 67 70 65 68 69 68 72 66 75 67 77 67 68 65 70 66 71 67 74 67 69 64 67 68 72 63 73 62 71 68 71 67 70 69 70 66 63 66 67 68 69 83 73 60 70 64 70 This data is heights for 50 men and 50 women. You want to know if the genders differ in height. What test do you use? Perform the test and present your results. HEIGHT (inches) Women Men 60 62 72 67 59 65 62 69 63 72 61 75 72 77 69 68 67 70 68 71 71 74 57 69 59 67 61 72 65 73 63 71 68 71 66 70 66 70 67 63 64 67 62 69 61 73 66 70 65 70 69 69 72 67 70 65 68 69 68 72 66 75 67 77 67 68 65 70 66 71 67 74 67 69 64 67 68 72 63 73 62 71 68 71 67 70 69 70 66 63 66 67 68 69 83 73 60 70 64 70

Explanation / Answer

HERE, WE USE THE 2-SAMPLE T TEST.

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Let

group 1 = women
group 2 = men

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.      
Calculating the means of each group,              
              
X1 =    65.88          
X2 =    69.94          
              
Calculating the standard deviations of each group,              
              
s1 =    4.321942118          
s2 =    3.253945799          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    50          
n2 = sample size of group 2 =    50          
Thus, df = n1 + n2 - 2 =    98          
Also, sD =    0.765079694          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    -5.30663672          
              
where uD = hypothesized difference =    0          
              
Now, the critical value for t is              
              
tcrit =    +/-   1.984467455
      
              
Thus, comparing t and tcrit, we decide to   WE REJECT THE NULL HYPOTHESIS.          
              
Also, using p values,              
              
p =    0.000000694557          
              
Comparing p < 0.05,    WE REJECT THE NULL HYPOTHESIS.          

There is significant evidence at 0.05 level that there is a difference between the mean heights of men and women. [conclusion]

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