Question

The mean heigh of American Males is 69.5 inches. The height of the 43 male presidents have a mean 70.78 inches and a standard deviation of 2.77 inches. Treating the 43 presidents as a simple random sample, determine if there is evidence to suggest that the US presidents are taller than the average American male. Use the a= 0.05 level of significance.

Answer 1

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, $\overline x$ = 70.78

The standard deviation, s = 2.77 inches

The number of male presidents = 43

The null hypothesis; H₀ μ = $\overline x$

The alternative hypothesis; Hₐ μ ≠ $\overline x$

The significance level, α = 0.05

The t test for the sample with unknown population standard deviation is given as follows;

$t=\dfrac{\bar{x}-\mu }{\dfrac{s }{\sqrt{n}}}$

Therefore, we have;

$t=\dfrac{70.78-69.5 }{\dfrac{2.77 }{\sqrt{43}}} \approx 3.0302$

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