The mean height of a 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 .

American presidents are taller than the average American man

Step-by-step explanation:

We have to:

H0: m = 69.5

Ha: m> 69.5

Since the population standard deviation is unknown and the hypothesis test of the population mean, the t-test should be used. Here the sample size is large, so we can assume that the sample distribution of the sample mean It is normal.

sd = 2.77, x = 70.78 and n = 43

Then the test statistics will be:

t = (x - m) / (s / n ^ (1/2))

replacing

t = (70.78 - 69.5) / (2.77 / 43 ^ (1/2))

t = 3.03

Here the test is correct and the degree of freedom of the test is df = n-1 = 43-1 = 42.

Critical approach:

So

alpha = 0.05, the critical value of the test is 1,682.

Rejection region:

If t> 1,682, reject the null hypothesis.

Since the value of the test statistics is greater than the critical value, we reject the null hypothesis.

P-value approach:

The p-value using the Excel function "= TDIST (3,030,42,1)" is:

p value = 0.0021

Since the p-value is less than α = 0.05, we reject the null hypothesis.

Which means that American presidents are taller than the average American man.