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### New Pension Plan

```
Date: 07/15/99 at 17:58:17
From: la tara mcgraw
Subject: Math - statistics

A sample of the employees of Carter industries regarding acceptance of
a new pension plan revealed the following:

opinion regarding new pension plan

age     superior   very good   good    fair    unsatisfactory
20-29      19         27        25      52          81
30-39      10         17        15      29          41
40-49      51         40        31      21          27
50-       142         81        16      9            8

Is there a relation between age and an employee's opinion of the new
plan? Test the .05 level.

```

```
Date: 07/15/99 at 19:21:16
From: Doctor Anthony
Subject: Re: Math - statistics

Table of Observed Frequencies.

Age  | Superior  V.good  Good   Fair   Unsatis.| Total
------|-----------------------------------------|---------
20-29 |    19       27     25     52       81   | 204
30-39 |    10       17     15     29       41   | 112
40-49 |    51       40     31     21       27   | 170
50-   |   142       81     16      6        8   | 253
-------|-----------------------------------------|--------
|   222      165     87    108      157   | 739

Table of Expected Values

Age  | Superior  V.good  Good   Fair   Unsatis.| Total
------|-----------------------------------------|---------
20-29 |    61       46     24     30       43   | 204
30-39 |    34       25     13     16       24   | 112
40-49 |    51       38     20     25       36   | 170
50-   |    76       56     30     37       54   | 253
-------|-----------------------------------------|--------
|   222      165     87    108      157   | 739

This is a 5 x 4 table so degrees of freedom = 4 x 3 = 12

The calculation of chi-squared is given in the next table

O     E     |O-E|     |O-E|^2     |O-E|^2/E
-----------------------------------------------
19    61                             28.9
27    46                              7.8
25    24                              0.04
52    30                             16.1
81    43                             33.6
10    34                             16.9
17    25                              2.6
15    13                              0.31
29    16                             10.6
41    24                             12.0
51    51                              0.0
40    38                              0.10
31    20                              6.0
21    25                              0.64
27    36                              2.25
142    76                             57.3
81    56                             11.2
16    30                              6.5
6    37                             26.0
8    54                             39.2
--------------------------------------------------
chi-squared = 278.04

And the tabular value of X^2 5% (degrees of freedom = 12) is 21.03

So our value is VERY significant and we reject the null hypothesis
that the opinion is independent of age.

- Doctor Anthony, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Statistics

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