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 ago
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