Homework SourseFor people over the age of 18 the cencus found the following
For people over the age of 18, the cencus found the following distrubition: 6.1% were between 18-19, 15% between 20-24, 13.5% between 25-29, 21.7% between 30-39, 15.3% between 40-49, 18.2% between 50-64, and 10.2% were 65+ years old. We wish to find out if jury selections are actually representative of the public. To do this, we will compare the observed data for many different juries to the census data given below.
Age Observed
18-19
23
20-24
96
25-29
134
30-39
293
40-49
297
50-64
380
65+
113
Total
1336
Run a goodness of fit test to determine if the observed data fits the distribution given by the census data.
| 18-19 | 23 |
| 20-24 | 96 |
| 25-29 | 134 |
| 30-39 | 293 |
| 40-49 | 297 |
| 50-64 | 380 |
| 65+ | 113 |
| Total | 1336 |
Solution
For people over the age of 18, the cencus found the following distrubition: 6.1% were between 18-19, 15% between 20-24, 13.5% between 25-29, 21.7% between 30-39, 15.3% between 40-49, 18.2% between 50-64, and 10.2% were 65+ years old. We wish to find out if jury selections are actually representative of the public. To do this, we will compare the observed data for many different juries to the census data given below.
Run a goodness of fit test to determine if the observed data fits the distribution given by the census data.
Null hypothesis: the observed data fits the distribution given by the census data.
Alternate hypothesis: the observed data does not fit the distribution given by the census data.
Goodness of Fit Test
observed
expected
O - E
(O - E)² / E
23
6.1*1336/100=81.496
-58.496
41.987
96
15*1336/100=200.400
-104.400
54.388
134
13.5*1336/100=180.360
-46.360
11.916
293
21.7*1336/100=289.912
3.088
0.033
297
15.3*1336/100=204.408
92.592
41.942
380
18.2*1336/100=243.152
136.848
77.019
113
10.2*1336/100=136.272
-23.272
3.974
1336
1336
231.260
Table value of chi square with 6 DF at 0.05 level = 12.59
Calculated Chi square 231.26 > table value 12.59
The null hypothesis is rejected.
We conclude that the observed data does not fit the distribution given by the census data
| Goodness of Fit Test | ||||
| observed | expected | O - E | (O - E)² / E | |
| 23 | 6.1*1336/100=81.496 | -58.496 | 41.987 | |
| 96 | 15*1336/100=200.400 | -104.400 | 54.388 | |
| 134 | 13.5*1336/100=180.360 | -46.360 | 11.916 | |
| 293 | 21.7*1336/100=289.912 | 3.088 | 0.033 | |
| 297 | 15.3*1336/100=204.408 | 92.592 | 41.942 | |
| 380 | 18.2*1336/100=243.152 | 136.848 | 77.019 | |
| 113 | 10.2*1336/100=136.272 | -23.272 | 3.974 | |
| Total | 1336 | 1336 | 231.260 |
