Question

multi-part question that i’m lost on.

data for q’s:

- 11 - A Full Clear aste Calibri (Body) B 1 U % C fx J7 WE Externalizing Scores-- 3rd grade 2.8333 1.5 1.1667 1.8333 1.3333 2.1667 1.1667 1.5 2.8333 1.6667 1.1667 1.3333 Reading Scores-- 5th grade 126.95 111.74 122.03 136.34 133.16 132.75 123.01 120.15 114.03 85.801 120.23 116.13 125.81 142.09 122.55 119.36 61.085 131.08 120.61 113.35 122.89 128.55 133.33 132.95 2.1667 2.8333 1.1667 1.6667 1.3333 1.1667 1.6667 1.3333 mt no OHNMOM Sheet

q’s:

Answer 1

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	2.8333	126.95	8.02758889	16116.3025	359.687435
	1.5	111.74	2.25	12485.8276	167.61
	1.1667	122.03	1.36118889	14891.3209	142.372401
	1.8333	136.34	3.36098889	18588.5956	249.952122
	1.3333	133.16	1.77768889	17731.5856	177.542228
	1	132.75	1	17622.5625	132.75
	2.1667	123.01	4.69458889	15131.4601	266.525767
	1.1667	120.15	1.36118889	14436.0225	140.179005
	1.5	114.03	2.25	13002.8409	171.045
	2.8333	85.801	8.02758889	7361.811601	243.099973
	1.6667	120.23	2.77788889	14455.2529	200.387341
	1.1667	116.13	1.36118889	13486.1769	135.488871
	1.3333	125.81	1.77768889	15828.1561	167.742473
	1	142.09	1	20189.5681	142.09
	2.1667	122.55	4.69458889	15018.5025	265.529085
	2.8333	119.36	8.02758889	14246.8096	338.182688
	3	61.085	9	3731.377225	183.255
	1.1667	131.08	1.36118889	17181.9664	152.931036
	1.6667	120.61	2.77788889	14546.7721	201.020687
	1.3333	113.35	1.77768889	12848.2225	151.129555
	1.1667	122.89	1.36118889	15101.9521	143.375763
	1.6667	128.55	2.77788889	16525.1025	214.254285
	1.3333	133.33	1.77768889	17776.8889	177.768889
	1.5	132.95	2.25	17675.7025	199.425
Total	40.3334	2895.976	76.83330002	355980.7801	4723.3446

Hypotheses are:

= 0

$H_{a}:\beta_{1}\neq 0$

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Here we need to use t-test for slope.

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Sample size: n 24 From table we have: (Σ . = 76.83330002- ((40.3334)^2 /24) 2 n = 9.05067 sST STy_(E»)* 355980.780126- ((2895.976)^2 /24) = 6535.90544 SP= Sx Σν- Σν) = 4723.3446043- ((2895.976* 40.3334) /24) = -143.511996

The slope is: SyT -143.511996/9.05067 = . b -15.8565 The intercept is: 1 (Ey-b^x) = (2895.976 - (-15.8565 * 40.3334)) / 24 bo 147.3134

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Test for slope:

The SSE is SSE y-bo>y-b^xy 355980.780126 - (147.3134 * 2895.976) - ( -15.8565 * 4723.3446043) 4260.422966 The standard error of estimate: SSE sqrt(4260.422966/(24-2)) - 2 SE = SE= 13.916 The standard error of slope is: SE sbi = 13.916/sqrt(9.05067)) sb, =4.6257

Level of significance: 0.05 Test is two tailed. Degree of freedom: df =n-2=22 Test Statistics: by-P (-15.8565 - 0)/4.6257 t = sb = -3.428 Critical value: Rejection Region 2.0739 -2.0739 or t > 2.0739, Reject H0 Ift Decision: Since test statistics lies in rejection region so we reject the null hypothesis P-value 0.0024 P-value: reject the null hypothesis Decision: Since p-value is less than level of significance so we Excel function for critical value: =TINV(0.05,22) =TDIST (3.428,22,2) Excel function for p-value:

Conclusion: There is significant relationship between the variables.