Question

What is the relationship between the attendance at a major league ball game and the total number of runs scored? Attendance figures in thousands) and the runs scored for 9 randomly selected games are shown below. Attendance 60 36 13 18 40 21 51 45 47 11 7 8 Runs 12 7 2 7 10 الا a. Find the correlation coefficient: r = Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: HO: ?v = 0 H: 70 The p-value is: (Round to four decimal places) c. Use a level of significance of a = 0.05 to state the conclusion of the hypothesis test in the context of the study. O There is statistically significant evidence to conclude that a game with higher attendance will have fewer runs scored than a game with lower attendance. There is statistically significant evidence to conclude that there is a correlation between the attendance of baseball games and the runs scored. Thus, the regression line is useful. O There is statistically insignificant evidence to conclude that there is a correlation between the attendance of baseball games and the runs scored. Thus, the use of the regression line is not appropriate. There is statistically significant evidence to conclude that a game with a higher attendance will have more runs scored than a game with lower attendance. d. r? (Round to two decimal places) (Round to two decimal places)

Answer 1

X 60 12 7 36 13 y2 144 49 4 49 100 720 252 26 2 7 18 40 21 51 45 47 3600 1296 169 324 1600 441 2601 2025 2209 10 3 11 7 8 126 400 63 561 315 376 121 49 64 331 67 14265 589 2839 Σx=331, Σx2 =14265, Σy=67, Σy] =589, Σxy=2839 Sx =Σx2 . Σα)? =14265 - (331)2 =2091.5556 n (67)2 S» -Σy? (Σν)? =589 - =90.2222 η 9 Σα)Σy Say =ΣΧΥ - 331*67 = 2839 - =374.8889 9 η

уху (Ex)Ey) a) Correlation coefficient r= n V(Ex2 - (Ena) = Sxy SxxSyy =0.863001 =0.86 b) Test hypothesis are Ho: P = 0 HP70 n-2 Test statistic t=r*. = 0.86* 1-72 9-2 = 4.459 1-(0.86)2 p-value=TIDTS(4.459,7,2)=0.00259 (Using excel) c) Sincep-value<0.05 hence reject the null hypothesis 2nd option is correct d) coefficient of determination r2 = 0.7448 = 0.74 or 74.48%

Using the excel the regression output is SUMMARY OUTPUT Regression Statistics Multiple R 0.863000618 R Square 0.744770066 Adjusted RS 0.708308647 Standard Err 1.81373379 Observation: 9 ANOVA df F 20.4262501 Significance F 0.002733651 Regression Residual Total SS MS 1 67.19481041 67.1948104 7 23.02741181 3.28963026 8 90.22222222 Intercept X Variable 1 Coefficients Standard Errol t Stat 0.852422439 1.578895819 0.53988517 0.179239269 0.039658734 4.51954092 P-value 0.606016743 0.002733651 Lower 95% Upper 95% -2.881072905 4.58591778 0.085461266 0.27301727