Question

the city collect a random sample of of times five of their traffic cameras caught someone speeding through a red light in a one year period. the following is the data collected, 750, 600, 8:20, 9:50, and 580. The planning commission for the city is claiming that the number of cars speeding through red lights has decreased from last year's average of 900 tickets. is it reasonable to conclude that that take its have decreased from last year? why?

Answer 1

The following table would be used to make the computations here as:

X	(X - Mean(X))^2
750	100
600	19600
820	6400
950	44100
580	25600
3700	95800

The last row gives the sum of those columns.

The sample mean and sample standard deviation here are computed as:

The test statistic now is computed here as:

For n - 1 = 4 degrees of freedom, we have from the t distribution:

p = P( t₄ < -2.31) = 0.0410

As the p-value here is 0.0410 < 0.05, therefore the test is significant here and we can reject the null hypothesis here and conclude that we have sufficient evidence here that  the number of cars speeding through red lights has decreased from last year's average of 900 tickets