Question

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 384 326 367 347 335 310 310 502 420 432 396 374 Foreign Born 100 81 84 82 95 84 59 91 69 101 102 83 Identify the null and alternative hypotheses for this test. A. Upper H 0​: Months of births of baseball players are independent of where they are born. Upper H 1​: Months of births of baseball players are dependent of where they are born. B. Upper H 0​: The frequency of births is dependent of the month. Upper H 1​: The frequency of births is independent of the month. C. Upper H 0​: The frequency of births is independent of the month. Upper H 1​: The frequency of births is dependent of the month. D. Upper H 0​: Months of births of baseball players are dependent of where they are born. Upper H 1​: Months of births of baseball players are independent of where they are born. Identify the test statistic. nothing ​(Round to three decimal places as​ needed.) Identify the​ P-value. nothing ​(Round to three decimal places as​ needed.) State the final conclusion that addresses the original claim. ▼ Reject Do not reject Upper H 0. There is ▼ sufficient not sufficient evidence to warrant rejection of the claim that months of births of baseball players are independent of whether they are born in America.

Answer 1

Solution :

Option A

Upper H 0​: Months of births of baseball players are independent of where they are born.

Upper H 1​: Months of births of baseball players are dependent of where they are born

	Jan	Feb	March	Apri	Ma	Jun	Jul	Aug	Sept	Oct	Nov	Dec	total
Born in America	384	326	367	347	335	310	310	502	420	432	396	374	4503
Foreign Born	100	81	84	82	95	84	59	91	69	101	102	83	1031
Total	484	407	451	429	430	394	369	593	489	533	498	457	5534

	Jan	Feb	March	Apri	Ma	Jun	Jul	Aug	Sept	Oct	Nov	Dec
Expected= (row total * column total)/ grand total	393.8294	331.1747	366.9774	349.0761	349.8898	320.5967	300.2542	482.5224	397.8979	433.7006	405.2212	371.8596
Expected= (row total * column total)/ grand total	90.17058	75.82526	84.02259	79.92392	80.11023	73.40332	68.74575	110.4776	91.1021	99.29942	92.77882	85.1404

((Observed - expected)^2)/(Expected)	0.245328	0.080857	1.39E-06	0.012347	0.633643	0.350252	0.316331	0.786236	1.227709	0.006668	0.209836	0.01232
((Observed - expected)^2)/(Expected)	1.071496	0.353153	6.07E-06	0.053927	2.767503	1.529761	1.381608	3.433969	5.362145	0.029124	0.916482	0.053809

P value = 0.035

P value > alpha

0.035 > 0.01

Do not reject Upper H 0

There is not sufficient evidence to warrant rejection of the claim that months of births of baseball players are independent of whether they are born in America.