Question

The mean height of American males is 69.5 inches. The heights of the 43 male U.S.
presidents *(Washington through Obama) 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 U.S. presidents are taller than the average American male. Use the α = 0.05 level
of significance. Use the classical and p-value method! Give an interpretation as well.

Answer 1

Hypotheses are:

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

Here we have following information:

So test statitics will be

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

Critical approach:

So for , critical value of the test is 1.682.

Rejection region:

If t > 1.682, then reject the null hypothesis.

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

P-value approach:

The p-value using excel function "=TDIST(3.030,42,1)" is:

p-value = 0.0021

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

Interpretation:

There is evidence to suggest that U.S. presidents are taller than the average American male.