Question

A high school runs a survey asking students if they participate in sports. The results are found below. Run an independence test for the data at α=0.01.

Freshmen Sophomores Juniors Seniors

Yes 75 88 55 42

No 30 28 38 40

Enter the test statistic - round to 4 decimal places.

Answer 1

hypothesis:-

participation in sports is independent of grade level.

participation in sports is dependent of grade level.

here we will do chi square test for independence.

the necessary calculation table:-

		freshmen	sophomores	juniors	seniors	row total
yes	observed frequency(Oi)	75	88	55	42	260
	expected frequency(Ei)	(105*260)/396 = 68.9394	(116*260)/396 = 76.1616	(93*260)/396 =61.0606	(82*260)/396 = 53.8384
		0.53280	1.84013	0.60155	2.60311
all	observed frequency(Oi)	30	28	38	40	136
	expected frequency(Ei)	(105*136)/396 = 36.0606	(116*136)/396 = 39.8384	(93*136)/396 =31.9394	(82*136)/396 =28.1616
		1.01859	3.51790	1.15002	4.97654
column total		105	116	93	82	396

the test statistic be:-

= (0.53280+1.84013+0.60155+2.60311+1.01859+3.51790+1.15002+4.97654)

degrees of freedom = (4-1)*(2-1) = 3

p value = 0.0010

[ in any blank cell of excel type =CHIDIST(16.2406,3) press enter...you will get 0.001012 ]

decision:-

p value = 0.0010 <0.01 (alpha)

so, we reject the null hypothesis.

conclusion:-

we conclude that participation in sports is dependent of the grade level at 0.01 level of significance.

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