This assignment illustrates the tests involving the two different C 2 tests cove

Question

This assignment illustrates the tests involving the two different C2 tests covered in sections 11.2 and 11.3.   Your solution will contain:
   - A clear statement of hypotheses
   - Statement of the test statistic and either p-value (or appropriate critical value)
   - Explicit statement of the statistical decision, along with a reason
   - A specific conclusion based on the statistical decision.

#1)   The table below lists the number of officers and enlisted personnel for women in the military.

Officers          Enlisted

Army               10,791               62,491

Navy               7 ,816               42,750

Marine Corps       932                 9,525

Air Force         11,819               54,344

At a = 0.05, is there sufficient evidence to conclude that a relationship exists between rank and branch if the Armed Forces?

Explanation / Answer

here null hypothesis: there is no relationship b/w  rank and branch

alternate hypothesis: There is relationship exists between rank and branch in the Armed Forces

for above test stat =654.272

degree of freedom =4-1=3

and p value =0.0000

as p vlaue is very low,we reject null hypothesis.

There is sufficent evidence to conclude that a relationship exists between rank and branch if the Armed Forces

Observed O Offiecrs Enlisted Total Army 10791 62491 73282 Navy 7816 42750 50566 Marine corps 932 9525 10457 Air Force 11819 54344 66163 Total 31358 169110 200468 Expected E=rowtotal*column total/grand total Offiecrs Enlisted Total Army 11463.061 61818.939 73282 Navy 7909.734 42656.266 50566 Marine corps 1635.725 8821.275 10457 Air Force 10349.479 55813.521 66163 Total 31358 169110 200468 chi square =(O-E)^2/E Offiecrs Enlisted Total Army 39.402 7.306 46.708 Navy 1.111 0.206 1.317 Marine corps 302.758 56.140 358.899 Air Force 208.657 38.691 247.348 Total 551.928 102.344 654.272

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