Question

Find T Statistic and P-value

A study of the effect of massage on boxing performance measured a boxer's blood lactate concentration (in mM) and perceived recovery (on a 28-point scale). On the basis of the information provided by the study, the data shown in the accompanying table were obtained for 16 five-round boxing performances in which a massage was given to the boxer between rounds. Conduct a test to determine whether blood lactate level (y) is linearly related to perceived recovery (x). Use a = 0.10. Click the icon to view the table of boxer blood data. i Boxer Blood Data Determine the correct null and alternative hypotheses. Choose the correct answer below. 0 Perceived Recovery O A. Ho: B1 * 0, Ha: B7 = 0 C. Ho: B1 = 0, Ha: B170 O E. Ho: B1 = 0, Hai By > 0 Blood Lactate Level 3.8 4.3 4.8 Find the test statistic. 4.1 t=] (Round to three decimal places as needed.) 5.0 5.3 4.2 2.4 م ي ة 6.0 6.5 Enter your answer in the answer box and then click Check Answer.

Answer 1

Answer:

from the given data

Obs.	XX	YY	Xi^2​	Yi^2​	Xi.Yi
1	3.8	8	14.44	64	30.4
2	4.3	8	18.49	64	34.4
3	4.8	11	23.04	121	52.8
4	4.1	12	16.81	144	49.2
5	5.0	12	25	144	60
6	5.3	12	28.09	144	63.6
7	4.2	13	17.64	169	54.6
8	2.4	16	5.76	256	38.4
9	3.9	17	15.21	289	66.3
10	5.3	17	28.09	289	90.1
11	5.8	18	33.64	324	104.4
12	6.0	18	36	324	108
13	5.9	23	34.81	529	135.7
14	6.3	23	39.69	529	144.9
15	5.5	22	30.25	484	121
16	6.5	25	42.25	625	162.5
Sum =	79.1	255	409.21	4499	1316.3

The sum of squares obtained from the table above are:

SSxx = = 400.21 (79.12 18.1594 $$y = = 4499 ) To (255) 434.9375 = 1316.3 -T (70.1) (255) = 55.6438

The slope and y-intercept coefficients are computed using the following formulas: B = SSxy SSxx 55.6438 18.1594 3.0642 Bo = Y - Bixx = 15.9375 -3.0642 x 4.9438 = 0.7889 Therefore, the regression equation is: Y = 0.7889 +3.0642X

SSE=   (SSxx * SSyy - SS²xy)/SSxx = 264.47

std error ,Se =    √(SSE/(n-2)) = 4.346

slope hypothesis test
Ho:   ß1=   0          
H1:   ß1╪   0          
n=   16              
alpha =   0.1              
estimated std error of slope =Se(ß1) = Se/√Sxx = 4.346 /√ 18.16 = 1.0198
                  
t stat = estimated slope/std error =ß1 /Se(ß1) =  3.0642 / 1.0198 = 3.005
                     
Degree of freedom ,df = n-2=   14              
p-value = 0.0095
decison :    p-value<α , reject Ho .