Answer: B) 31.348
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Work Shown:
We will never use the alpha = 0.05 value when computing the test statistic. So we can ignore alpha for this particular problem.
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n = 40 is the sample size.
s = 2.6 is the sample standard deviation
[tex]\sigma[/tex] = sigma = 2.9 is the population standard deviation (ie the claimed standard deviation for all the pay phones)
Test Statistic for chi-square
[tex]\chi^2 = \frac{(n-1)*s^2}{\sigma^2}\\\\\chi^2 = \frac{(40-1)*(2.6)^2}{(2.9)^2}\\\\\chi^2 = \frac{39*6.76}{8.41}\\\\\chi^2 = \frac{263.64}{8.41}\\\\\chi^2 \approx 31.3483947681332\\\\\chi^2 \approx 31.348\\\\[/tex]
