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


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