Respuesta :
Answer:
Sons are taller than their fathers.
Step-by-step explanation:
The t-statistic for difference of mean is given by,
[tex]t=\dfrac{\bar{x_{1}}-\bar{x_{2}}}{\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}}[/tex]
Calculating Mean of Son's height = [tex]\bar{x_{1}}[/tex] = 74.22
Mean of Father's height = [tex]\bar{x_{2}}[/tex] = 72.5
Variance of Son's height = [tex]{s_{1}^{2}}[/tex] = 17.155
Variance of Father's height = [tex]{s_{2}^{2}}[/tex] = 5.69
and n₁ = n₂ = 6
⇒ [tex]t=\dfrac{74.22}-\bar{72.5}{\sqrt{\frac{17.55}{6}+\frac{5.69}{6}}[/tex]
Using this formula, we get, t = 0.80306.
Using t-table, p-value = 0.220306 with 10 degree of freedom.
and α = 0.10
Since, the p-value is greater than alpha (p > .10), then we fail to reject the null hypothesis, and we say that the result is statistically non-significant.
