The contingency table below was constructed using data from a sample of Penn Sta

Question

The contingency table below was constructed using data from a sample of Penn State employees. Use this table to answer the following questions. A. Compute the row and column totals: B. Compute the expected value for the female - faculty cell by hand (i.e., do NOT use Minitab Express). C. How would you interpret the value that you computed in part B for a friend with no knowledge of statistics? D. Are biological sex and position independent? Use the five-step hypothesis testing procedure. Step 1: Step 2: Step 3: Step 4: Step 5:

Explanation / Answer

A.

B. Expected Value for the femalle - faculty cell = 64*97/196 = 31.67

C.

D.

Step.1 write null and alternative hypotheses.

Null Hypothesis : H0 : Biological Sex and Position are independent.

Alternative Hypothesis : Ha : Biological Sex and Position are dependent.

Step 2. Calculate an appropriate test statistic.

X2 = (25 - 31.67)2 / 31.67 + (72 - 65.33)2 / 65.33 + (39 - 32.33)2 /32.33 + (60 - 66.67)2 / 66.67 = 5.13

Step 3. Determine a p-value associated with the test statistic.

X2 cr = 3.841 at alpha = 0.05 and dF = 1

X2 > X2 cr

p - value = 0.042

Step 4. Decide between the null and alternative hypotheses.

if p < 0.05 then so we will reject the null hypothesis.

Step 5. State a "real world" conclusion.

We shall conclude that biological sex and position are dependent.

Position Faculty Staff Total Biological Female 25 72 97 Sex Male 39 60 99 Total 64 132 196

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