Question

Report a) the appropriate statistical test or estimation procedure to use, b) the null and alternate hypotheses, c) the test statistic, d) the P value, e) whether you accept or reject the null, then f) a sentence or two about what the results mean.

Is there a difference between height of male children and female children? Show results using a parametric test and also the results using the appropriate non-parametric test. Which is the most appropriate test to use and why?

male = 1

female = 2

Height is in cm

child_sex	child_ht
1	130
1	135
1	139
1	138
2	125
2	129
1	133
1	128
2	120
2	140
1	144
1	150
2	134
1	132
2	131
1	128
1	139
2	136
1	161
1	163
2	145
2	141
1	154
1	159
1	132
1	138
1	143
2	134
2	140
1	148
1	140
2	133
2	134
1	151
1	157
1	145
1	161
1	154
2	159
1	132
1	134
1	138
1	145
2	134
2	123
1	136
1	133
1	167
1	158
2	149
2	143
2	145
1	147
1	142

Answer 1

a)

2 Sample t test

b)

Ho :   µ1 - µ2 =   0                  
Ha :   µ1-µ2 ╪   0      

c)
                          
Level of Significance ,    α =    0.05                  
                          
Sample #1   ---->   Male
mean of sample 1,    x̅1=   143.83                  
standard deviation of sample 1,   s1 =    11.08                  
size of sample 1,    n1=   35                  
                          
Sample #2   ---->   Female
mean of sample 2,    x̅2=   136.58                  
standard deviation of sample 2,   s2 =    9.44                  
size of sample 2,    n2=   19                  
                          
difference in sample means =    x̅1-x̅2 =    143.8286   -   136.6   =   7.25  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    10.5426                  
std error , SE =    Sp*√(1/n1+1/n2) =    3.0042                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   7.2496   -   0   ) /    3.00   =   2.413

d)
                          
Degree of freedom, DF=   n1+n2-2 =    52                  

p-value =        0.019376   (excel function: =T.DIST.2T(t stat,df) )              

e)

Conclusion:     p-value <α , Reject null hypothesis     

f)
                          
There is enough evidence that male mean and female mean are different.

Thanks in advance!

revert back for doubt

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