Question

Many track runners believe that they have a better chance of winning if they start in the inside lane that is closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is Lane 2, and so on until the outermost lane, Lane 6. The table displays the starting positions for the winners of 240 competitions. Calculate the chi-square test statistic X2 used to test the claim that the probability of winning is the same regardless of starting position.



Starting Position 1 2 3 4 5 6

Number of Wins 33 44 32 36 45 50



a.12.592

b.15.541

c.9.326

d.6.750

Answer 1

Answer:

d) 6.750

The chi - square value = 6.750

Step-by-step explanation:

Given data

Starting Position              1           2            3           4            5              6  

Number of Wins (O)       33        44            32         36         45           50

Step(i) :-

mean = $\frac{33+44+32+36+45+50}{6} = \frac{240}{6} =40$

Expected frequency = 40

Number of Wins (O)      :     33        44            32         36         45           50

Expected frequency(E)   :   40         40           40         40          40          40

(O - E )                              :    -7          4              -8           -4           5            10

(O-E)²                               :     49         16           64          16          25          100

$\frac{(O-E)^2}{E}$                              :      1.225    0.4       1.6         0.4         0.625     2.5  

Step(ii):-

The χ² test

     χ²   =    ∑   $\frac{(O-E)^2}{E}$

  χ²  =  1.225 + 0.4 + 1.6 + 0.4 +0.625 +2.5 = 6.75

The chi - square value = 6.750

Final answer:-

The chi - square value = 6.750