Thread: Another Goodness of Fit test....GRRRR

I'm so confused with this goodness of fit stuff. I'm trying to solve the following problem...can anyone help??

The safety director of Honda USA took samples at random from the file of minor accidents and classified them according to the time the accident took place. Using the goodness-of-fit test and the .01 level of significance, determine whether the accidents are evenly distributed (uniform) throughout the day. Write a brief explanation of your conclusion. (accidents)


Time
Number of Accidents

8 up to 9 AM

6

9 up to 10 AM

6

10 up to 11 AM

20

11 up to 12 PM

8

1 up to 2 PM

7

2 up to 3 PM

8

3 up to 4 PM

19

4 up to 5 PM

6

Originally Posted by sebchase0625

I'm so confused with this goodness of fit stuff. I'm trying to solve the following problem...can anyone help??

The safety director of Honda USA took samples at random from the file of minor accidents and classified them according to the time the accident took place. Using the goodness-of-fit test and the .01 level of significance, determine whether the accidents are evenly distributed (uniform) throughout the day. Write a brief explanation of your conclusion. (accidents)


Time
Number of Accidents

8 up to 9 AM

6

9 up to 10 AM

6

10 up to 11 AM

20

11 up to 12 PM

8

1 up to 2 PM

7

2 up to 3 PM

8

3 up to 4 PM

19

4 up to 5 PM

6

You can use a chi-square test for goodness of fit. The null hypothesis is

H0: $\displaystyle p_1 = p_2 = p_3 = p_4 = p_5 = p_6 = p_7 = p_8 = \frac{1}{8}$

where $\displaystyle p_i$ is the probability of an accident in the ith hourly interval for i = 1, 2, ...... 8.

The chi-square test statistic will have 8 - 1 = 7 degrees of freedom.

Now calculate the value of $\displaystyle X^2$ and test it for significance at the 0.01 level: $\displaystyle X^2 = \sum_{i=1}^{8} \frac{(n_i - n p_i)^2}{np_i}$

where n is the total number of accidents and $\displaystyle n_i$ is the number of accidents in the ith hourly interval (you should be familiar with this formula and where it comes from).