variance A random sample of the number of games played by individual NBA scoring

Question

variance

    A random sample of the number of games played by individual NBA scoring leaders is shown below. If a sports analyst argues that this sample variance is no different from 40 at = .05, is she correct? Assume, of course, that the number of games played variable is normally distributed.   Use the P-value method. (Round to 4 digits.)

(Hint: this is a two-tailed test. So compute the P/2 value corresponding to the Chi-square test statistic and compare it with /2. Which tail of the Chi-square distribution to use? Compare your computed sample variance with the hypothesized population variance. If s2 > 2 , use right tail; if less, use left tail.)

            88        86        80        74        82       

            79        82        78        60        75

Explanation / Answer

Data:     

n = 10    

^2 = 40    

s^2 = 60.93    

Hypotheses:     

Ho: ^2 = 40    

Ha: ^2 40    

Decision Rule:     

Degrees of freedom = n - 1 =    10 - 1 = 9

= 0.05    

Reject Ho if p- value < 0.05

Test Statistic:     

2 = (n - 1) s^2 / s^2 =   (10 - 1) * 60.93 / 40 = 13.70925

p- value = 1.733899691

Since the p- value > 0.05, we fail to reject Ho

There is no sufficient evidence that ^2 40

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