Answer:
There is sufficient statistical evidence to suggest that the US presidents are taller than the average American male
Step-by-step explanation:
The given parameters are;
The mean height of American Males, μ = 69.5 inches
The mean height of 43 male presidents, [tex]\overline x[/tex] = 70.78
The standard deviation, s = 2.77 inches
The number of male presidents = 43
The null hypothesis; H₀ μ = [tex]\overline x[/tex]
The alternative hypothesis; Hₐ μ ≠ [tex]\overline x[/tex]
The significance level, α = 0.05
The t test for the sample with unknown population standard deviation is given as follows;
[tex]t=\dfrac{\bar{x}-\mu }{\dfrac{s }{\sqrt{n}}}[/tex]
Therefore, we have;
[tex]t=\dfrac{70.78-69.5 }{\dfrac{2.77 }{\sqrt{43}}} \approx 3.0302[/tex]
The degrees of freedom, df = n - 1 = 43 - 1 = 42
The critical 't' value = 2.0181
Therefore, given that the t test value is larger than the critical-t, we reject the null hypothesis, therefore, there is sufficient statistical evidence to suggest that the US presidents are taller than the average American male
