Question
In: Statistics and Probability
The data below show sport preference and age of participant from a random sample of members...
The data below show sport preference and age of participant from a random sample of members of a sports club. Test if sport preference is independent of age at the 0.02 significant level.
H0: Sport preference is independent of age
Ha: Sport preference is dependent on age
| 18-25 | 26-30 | 31-40 | 41 and over | |
|---|---|---|---|---|
| Tennis | 43 | 60 | 56 | 44 |
| Swimming | 58 | 76 | 50 | 63 |
| Basketball | 74 | 61 | 65 | 49 |
a. Complete the table: Give all answers as decimals rounded to 4 places.
| Observed Frequency |
Expected Frequency |
(O−E)2E(O-E)2E |
|---|---|---|
| 43 | ||
| 60 | ||
| 56 | ||
| 44 | ||
| 58 | ||
| 76 | ||
| 50 | ||
| 63 | ||
| 74 | ||
| 61 | ||
| 65 | ||
| 49 | ||
| Total |
(b) What is the chi-square test-statistic for this data?
Solutions
Expert Solution
please rate. Thanks !!
Below is the table.
| 18-25 | 26-30 | 31-40 | 41 - over | Total | |
| Tennis | 43 | 60 | 56 | 44 | 203 |
| Swimming | 58 | 76 | 50 | 63 | 247 |
| Basket ball | 74 | 61 | 65 | 49 | 249 |
| Total | 175 | 197 | 171 | 156 | 699 |
Below is the contingency table :
| row | Col | fo (observed freq.) | fe (expected freq.) | (fo - fe) | (fo - fe)^2 | (fo - fe)^2/fe |
| 1 | 1 | 43 | 50.82260372 | -7.8226 | 61.193129 | 1.204053403 |
| 1 | 2 | 60 | 57.21173104 | 2.78827 | 7.7744438 | 0.13588898 |
| 1 | 3 | 56 | 49.66094421 | 6.33906 | 40.183628 | 0.809159572 |
| 1 | 4 | 44 | 45.30472103 | -1.3047 | 1.702297 | 0.037574384 |
| 2 | 1 | 58 | 61.83834049 | -3.8383 | 14.732858 | 0.238247947 |
| 2 | 2 | 76 | 69.61230329 | 6.3877 | 40.802669 | 0.586141635 |
| 2 | 3 | 50 | 60.4248927 | -10.425 | 108.67839 | 1.798569812 |
| 2 | 4 | 63 | 55.12446352 | 7.87554 | 62.024075 | 1.125164236 |
| 3 | 1 | 74 | 62.33905579 | 11.6609 | 135.97762 | 2.181258892 |
| 3 | 2 | 61 | 70.17596567 | -9.176 | 84.198346 | 1.199817417 |
| 3 | 3 | 65 | 60.91416309 | 4.08584 | 16.694063 | 0.274058813 |
| 3 | 4 | 49 | 55.57081545 | -6.5708 | 43.175616 | 0.776947672 |
| sum | 10.36688276 |
orchestra answered 3 years agoRelated Solutions
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Basketball
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The data below show sport preference and age of participant from a random sample of members...
The data below show sport preference and age of participant from
a random sample of members of a sports club. Test if sport
preference is independent of age at the 0.02 significant level.
H0: Sport preference is independent of age
Ha: Sport preference is dependent on age
18-25
26-30
31-40
41 and over
Tennis
40
60
58
44
Swimming
59
76
50
66
Basketball
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61
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53
a. Complete the table: Give all answers as decimals rounded to 4...
The data below show sport preference and age of participant from a random sample of members...
The data below show sport preference and age of participant from
a random sample of members of a sports club. Test if sport
preference is independent of age at the 0.05 significant level.
H0: Sport preference is independent of age
Ha: Sport preference is dependent on age
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59
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