Question

Suppose a teacher recorded the attendance of her students in a recent statistics class because she wanted to investigate the linear relationship between the number of classes they missed and their final grades. The accompanying table shows these data for a random sample of nine students. Complete parts a through c. Click the icon to view the table showing missed classes and final grade. Using a = 0.01, test the significance of the regression slope. The hypotheses for this test are Ho: B4 = 0 and Hy: B4*0. The test statistic is (Type an integer or decimal rounded to two decimal places as needed.) The p-value is (Type an integer or decimal rounded to three decimal places as needed.) the null hypothesis. There sufficient evidence to conclude that Therefore, at the 0.01 level of significance, the slope is zero. b. Construct a 99% confidence interval for the population slope. The confidence interval is (O. (Type integers or decimals rounded to three decimal places as needed.) c. What conclusions about missed classes and final grade can be drawn from these results? The conclusion is that there a linear relationship between missed classes and final grade because the null hypothesis rejected and because the confidence interval for ti population slope VO.
Missed Classes Final Grade

4 75

6 80

1 91

4 71

0 95

2 83

0 91

5 86

2 96

Answer 1

Hese, data is, the given missed Final classes(y) arrades (9) 4 75 X4 ŷ 300 2 (y-ý) 44.2185 15-0288 2 6 80 480 81.6497 76.1233 89.9393 81.6497 91 91 1:1251 4 113.4161 71 284 5 5.2785 95 92.7025 871761 6 2 83 166 17.4398 2.8985 o 7 91 92.7025 8 5 86 430 78.8865 87:1761 50.6019 77.8612 2 9 192 96 Hese, nag ZX = 24 = 2.667 = 168 9 = 85. 333 2x²=102 Iy2 = 66154 Ey = Exy = 1943 find Begagsion eq? ŷ= bothix ity - (17) (ay {x² - (24) ² so b = aty 2 1943 - 2048 102-64 - -105 38 b = -2.7632

bo ý -5, - 85333 - (-24632) ( 2.66+) = 85.333 + 7.3695 5o = 92.7025 so - 50+5 = 927025 2.7632x Here, sse - 2 cy-ŷ)? ose 327.8684 & MSE = SSE D-2 た 327.8684 g-2 827.8684 7 MSE = = 46.8383 & se(6) rase SS 46.8383 38 - 1:110219 = 1.1102 Secb Find, using 2 -0.01 pegaession test signi 6 cance of sbpe . Hipothesis is , Ho: Bi=0 Hi: Bio. vs

3 The statistic is, Lest E bı - Bi sech) h Sech) 2.7682 1.1102 2-48892 Ans. t = -2.49 4 P. value p.value -p [I Łl >-2-49) = 0.041597 Hes d.Fan-2 2 = 0.01 Ans Pvalue -0.042 Therefore, Accept 2 at 0.01 level of significance the bypothesis there is sufficient evidence to condude the slope equal not that zen. construct ggf. coofidence interval for the pop wario Slope 6 + Eco- 24/2. = C sec62) Here, to-0197 = 3.4995 - (-2.4632 + (3:4995) 11102))

2.7632 - 3.885) 2.7632 t 8.8851) (-2.1 - 2-7632 +3.885)) 커 (-6 -6.648, 1.122 Ans. confidence Interval is, - 6.6483, 1. 1219 - |-6.648 1.122 Os the what classes From conclusions about Final grades can be desults ? missed drawn and these + no The conclusions that the those as Linear Hlahonship beroeen missed classes Final grodes benacese the hypothesis not swej rejected and becouse the Confidence interal for the popwarm Slope between o