Question

# Chi-Square test for a normal distribution. The South Bend Station of the South Shore Railroad is...

Chi-Square test for a normal distribution.

The South Bend Station of the South Shore Railroad is having financial difficulties. The daily number of riders is believed to be normally distributed and the Railroad needs to know the distribution for scheduling. A sample of the number of riders for a 30 day period resulted in a sample mean of 24.5 and the sample standard deviation was 3. The actual data for the 30 day period is given below. Does it fit a normal distribution? Use a 10% significance level. 18, 25, 26, 27, 25, 20, 22, 23, 25, 25, 28, 22, 27, 20, 19, 31, 26, 27, 25, 24, 21, 29, 28, 22, 24, 24, 25, 25, 26, 26.

a) Ho :

Ha :

b) Determine the intervals: (use the Empirical Rule)

c) Bin the data using the intervals: Interval Tally fi E (n∙pi)

d) Calculate the test statistic:

e) Critical Value from the table:

f) Conclusion:

Ho : given data follow normal distribution

Ha: given data does not follow normal distribution

Expected value are in Ei column

TS = 3.2692

critical value for 10% alpha = 7.7794

since TS < critical value

we fail to reject the null hypothesis