Respuesta :
Answer:
The weight of an adult male who is 158 cm tall is 59.32 kg.
Step-by-step explanation:
The regression equation representing the relationship between height and weight of a person is:
[tex]\hat y=-105+1.04 x[/tex]
Here,
y = weight of a person (in kg)
x = height of a person (in cm)
The information provided is:
[tex]\bar x=167.77\ \text{cm}\\\bar y=81.54\ \text{cm}\\r(X, Y)=0.201\\p-value=0.045[/tex]
The significance level of the test is, α = 0.01.
The hypothesis to test the significance of the correlation between height and weight is:
H₀: There is no relationship between the height and weight, i.e. ρ = 0.
Hₐ: There is a relationship between the height and weight, i.e. ρ ≠ 0.
Decision rule:
If the p-value of the test is less than the significance level, then the null hypothesis will be rejected and vice-versa.
According to information provided:
p-value = 0.045 > 0.01
The null hypothesis will not be rejected at 1% level of significance.
Thus, concluding that there is no relationship between the height and weight.
Compute the weight of an adult male with height, x = 158 cm as follows:
[tex]\hat y=-105+1.04 x[/tex]
[tex]=-105+(1.04\times 158)\\=-105+164.32\\=59.32[/tex]
Thus, the weight of an adult male who is 158 cm tall is 59.32 kg.
