Th table to the ght shows tne number o mala students who played on a sports team

Question

Th table to the ght shows tne number o mala students who played on a sports team n grades 9 through 12 or a random sample 0 6 high schools in a state. At = 001 can you reject the claim hat he mean numbers offe male students ade Grade who played on a sports team are equal for all grades? Perform a one-way ANOVA test by completing parts a through d. Assume that eachsample is drawn from a normal population, that the samples are independent of each other, and that tha 9 10 111 populatlons have the same varlances. 92 77 6 65 64 51 5649 91 87877 133 125 115 102 110 104 688 t ldenty the degees of freedom for the narmeratorand tor the denominator determine the crmcal volue and determine the rejection region The degrees af teed rn for the tuner aardfN:la and the de rees artseedorn fer the dona inator dfD The critical value is Fo. Round to two decimal places as nosdad) The ejection ion s F Round to two decimal places (c) Calculte the tust statistic. needed ) Round to three decimel places as needed d) Decide to nject or fal so reject the null hy pothesis and Interpret the decision in the connext of the orginal claim Choose the comect decision below Since F is not i,najectien regen fal to rejee My Since F is not ine nejectien regkon nejectM C. Since Fis h the ,ejection segon. fal, to reject Mg O D. Since F is not in the nejection region, neject H Interpret te decision lhe context of the orignal claim

Explanation / Answer

Sol:

ANova one way

H0:All 4 group emans are equal

H1:atleast one of the emans are different.

Df fornumerator=3

Df for denominator=20

F crit=4.94

F statistic=0.507

F statistic<F Crit

Fail to Reject Ho

Since F isnot in the rejection Region fail to reject H0

Anova: Single Factor SUMMARY Groups Count Sum Average Variance Grade9 6 533 88.83333 870.1667 Grade10 6 502 83.66667 780.6667 Grade11 6 480 80 650 Grade12 6 423 70.5 529.1 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 1076.833 3 358.9444 0.507354 0.681664 4.938193 Within Groups 14149.67 20 707.4833

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