The following table shows the number of serviced orders n i , during time interv

Question

The following table shows the number of serviced orders ni, during time intervals and the theorectial number of serviced orders ñi, in the same time intervals given the assumption that the servicing time is exponentially distributed. Based on data given in the table, evaluate the value of the test criterion (test statistic). Make the decision (is the assumption about exponential distribution correct or not) at the significance level of 0.05. Explain.

Actual number   ni 23 10 27 4 25 7 9

Theoretical number   ñ 15 15 15 15 15 15 15

1. What is the number of groups?

m=

2. What is the number of degree of freedom in case of an exponential distribution (show also formula)?

k=

3. What is the critical point for test criterion at the significance level? (Use degree of freedom table, see Google)

  X2critical =

4. What is the test criterion (its formula and calculations)?

X2 =

5. Your decision (explain it):

Explanation / Answer

1. What is the number of groups?

m= 7, the total number of groups

2. What is the number of degree of freedom in case of an exponential distribution (show also formula)?

k= 15*7-7 = 105-7 = 98

3. What is the critical point for test criterion at the significance level? (Use degree of freedom table, see Google)

  X2critical =72.5009

4. What is the test criterion (its formula and calculations)?

X2 = 36.93333

5. Your decision (explain it):Since the observed value is less than the critical value, we can't reject the null hypothes and conclude the fitted distribution is a good one.

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