Question: A study of potential age discrimination considers promotions among middle–level administrators in a public university. The data are as follows:

1. (2 points) Find the expected number for each cell of the crosstabs table under the hypothesis of independence.

   Row variable	Under 30	30 - 39	40 - 49	50 and Over	Total
   Promoted	16	22.4	25.6	16	80
   Not Promoted	34	47.6	54.4	34	170
   Total	50	70	80	50	250

2. (1 point) What are the degrees of freedom equal to for this problem?
3. (2 points) Is there a statistically significant relationship between age and promotions, using \[\alpha =0.05\] ?

   p -Value

   0.004582

   
   The Chi-Square statistics is \({{\chi }^{2}}=12.025\), and the corresponding p-value is p = 0.004582. This means that we reject the null hypothesis of independence.
   If the data are combined as follows:

   Age
   	Up to 39	40 and Over	Total
   Promoted	38	42	80
   Not promoted	82	88	170
   Totals	120	130

4. (2 points) Can the hypothesis of independence be rejected using a reasonable \[\alpha \] ?

   p -Value

   0.913558

   
   The p-value is now p = 0.914, which means that that no reasonable \(\alpha \) will reject the null hypothesis of independence.
5. (3 points) What is the effect of combining age categories? Compare the answers to those obtained from the data that used the four-category age variable.

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