Question

For each of the following questions, report 1) the appropriate statistical test or estimation procedure to use, 2) the null and alternate hypotheses, 3) the test statistic, 4) the P value, 5) whether you accept or reject the null, then 6) a sentence or two about what the results mean.

Also answer this subpart: What is the relationship between age and height of children? Display data using one graph.

child_age	child_ht
5	130
7	135
9	139
8	138
7	125
8	129
5	133
4	128
4	120
10	140
10	144
12	150
11	134
5	132
8	131
7	128
7	139
9	136
13	161
13	163
14	145
12	141
11	154
11	159
5	132
6	138
7	143
6	134
8	140
9	148
7	140
7	133
9	134
10	151
10	157
12	145
13	161
12	154
13	159
12	132
6	134
7	138
8	145
7	134
5	123
5	136
5	133
14	167
12	158
12	149
8	143
9	145
7	147
6	142

Answer 1

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	467	7629	430.3148148	6426.8	1283.28
mean	8.65	141.28	SSxx	SSyy	SSxy

sample size ,   n =   54          
here, x̅ = Σx / n=   8.65   ,     ȳ = Σy/n =   141.28  
                  
SSxx =    Σ(x-x̅)² =    430.3148          
SSxy=   Σ(x-x̅)(y-ȳ) =   1283.3          
                  
estimated slope , ß1 = SSxy/SSxx =   1283.3   /   430.315   =   2.9822
                  
intercept,   ß0 = y̅-ß1* x̄ =   115.4874          
                  
so, regression line is   Ŷ =   115.4874   +   2.9822   *x
                  
SSE=   (SSxx * SSyy - SS²xy)/SSxx =    2599.863          
                  
std error ,Se =    √(SSE/(n-2)) =    7.071          
                  
correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.7717

2)

slope hypothesis test               tail=   2
Ho:   ß1=   0          
H1:   ß1╪   0     

3)

n=   54              
alpha =   0.05              
estimated std error of slope =Se(ß1) = Se/√Sxx =    7.071   /√   430.31   =   0.3409
                  
t stat = estimated slope/std error =ß1 /Se(ß1) =    2.9822   /   0.3409   =   8.7489

4)
                  
t-critical value=    2.007   [excel function: =T.INV.2T(α,df) ]          
Degree of freedom ,df = n-2=   52              
p-value =    0.0000              

5)

decison :    p-value<α , reject Ho              

6)

Conclusion:   Reject Ho and conclude that slope is significantly different from zero  

7)

Relationship is moderate and positive

THANKS

revert back for doubt

please upvote