Question
In: Statistics and Probability
An author argues that more American-born baseball players have birth dates in the months immediately following...
An author argues that more American-born baseball players have birth dates in the months immediately following July 31 because that was the age cutoff date for nonschool baseball leagues. The table below lists months of births for a sample of American-born baseball players and foreign-born baseball players. Using a 0.01 significance level, is there sufficient evidence to warrant rejection of the claim that months of births of baseball players are independent of whether they are born in America? Do the data appear to support the author's claim?
|
Jan. |
Feb. |
March |
April |
May |
June |
July |
Aug. |
Sept. |
Oct. |
Nov. |
Dec. |
||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
Born in America |
387 |
327 |
363 |
343 |
334 |
313 |
315 |
503 |
422 |
436 |
397 |
369 |
|
|
Foreign Born |
100 |
81 |
85 |
81 |
95 |
83 |
59 |
92 |
70 |
101 |
103 |
82 |
Identify the test statistic.
Identify the P-value.
State the final conclusion that addresses the original claim.
Solutions
Expert Solution
Null hypothesis: Ho: months of births of baseball players are independent of whether they are born in America or not
Alternate hypothesis: Ho: months of births of baseball players are dependent of whether they are born in America or not
| Applying chi square test of independence: |
| Expected | Ei=row total*column total/grand total | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec | Total |
| Boy | 396.30 | 332.01 | 364.56 | 345.03 | 349.10 | 322.25 | 304.34 | 484.18 | 400.37 | 436.98 | 406.88 | 367.00 | 4509 | |
| Girl | 90.70 | 75.99 | 83.44 | 78.97 | 79.90 | 73.75 | 69.66 | 110.82 | 91.63 | 100.02 | 93.12 | 84.00 | 1032 | |
| total | 487 | 408 | 448 | 424 | 429 | 396 | 374 | 595 | 492 | 537 | 500 | 451 | 5541 | |
| chi square χ2 | =(Oi-Ei)2/Ei | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec | Total |
| Boy | 0.2181 | 0.0756 | 0.0067 | 0.0120 | 0.6531 | 0.2653 | 0.3732 | 0.7313 | 1.1690 | 0.0022 | 0.2397 | 0.0109 | 3.7571 | |
| Girl | 0.9530 | 0.3304 | 0.0292 | 0.0522 | 2.8535 | 1.1591 | 1.6304 | 3.1953 | 5.1076 | 0.0097 | 1.0474 | 0.0475 | 16.4153 | |
| total | 1.1711 | 0.4060 | 0.0359 | 0.0642 | 3.5066 | 1.4243 | 2.0035 | 3.9267 | 6.2766 | 0.0119 | 1.2871 | 0.0584 | 20.1724 | |
| test statistic X2 = | 20.1724 | |||||||||||||
| degree of freedom(df) =(rows-1)*(columns-1)= | 11 | |
from excel p value =chidist(20.1724,11) =0.0430
since p value >0.01 , we can not reject null hypothesis
we do not have convincing evidence to conclude that
months of births of baseball players are dependent of whether they are born in America or not
orchestra answered 1 year agoRelated Solutions
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