Question

Perform the indicated goodness-of-fit test using the P-value method. Be sure to state the hypotheses and the significance level , to compute the value of the test statistic, to obtain the P-value, and to state your conclusion. 3) The U.S. Department of Defense provides data on the distribution of military personnel on active duty by branch of service. Below is a table giving the percentage distribution for 1985. Branch of Service Percentage Army 36.3 Navy 26.5 Marine Corps 9.2 Air Force 28.0 A random sample of 325 military personnel currently on active duty gave the following statistics. Branch of Service Frequency Army 102 Navy 101 Marine Corps 40 Air Force 82 At the 5% significance level, do the data provide evidence that the current distribution of military personnel on active duty differs from the 1985 distribution? *Please show all work

Answer 1

Ho: The current distribution is the same as the 1985 distribution

Ha: The current distribution is different from the 1985 distribution

	Observed (O)	Expected (E)	(O - E)^2 /E
Army	102	117.975	2.1632
Navy	101	86.125	2.5691
Marine Corps	40	29.9	3.4117
Air Force	82	91	0.8901
		χ2 =	9.0341
		Df = 3
		p- value =	0.0288

Since 0.0288 < 0.05, we reject Ho

The data provide evidence that the current distribution of military personnel on active duty differs from the 1985 distribution