and the risk of accidents at a junction. Suppose we observe the following frequenc distribution of the mumber of accidents in 150 weeks. Number of Accidents 0 Observed frequency 1 3. 4. 6 7+ 50 30 24 30 10 5 1

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Transport engineers are interested to study the pattern

and the risk of accidents at a junction. Suppose we observe the following frequency
distribution of the mumber of accidents in 150 weeks.
Number of Accidents
Observed frequency
0.
1
3.
4.
67+
50
30 24
30
10 5
1
(a) Find an estimate (to four decimal places) of the average number of accidents in a
week.
(b) Perform a goodness of fit test at the 5% significance level of the null hypothesis
that the observed number of accidents follow a Poisson distribution.
Hint: Use the estimate (to four decimal places) you computed in (a) and report
the expected frequency and observed value of the statistic to four decimal places. [
(c) What is the p-value of your test in (b)? Does the p-value indicate that there is
evidence against the null hypothesis?
Transcribed Image Text:and the risk of accidents at a junction. Suppose we observe the following frequency distribution of the mumber of accidents in 150 weeks. Number of Accidents Observed frequency 0. 1 3. 4. 67+ 50 30 24 30 10 5 1 (a) Find an estimate (to four decimal places) of the average number of accidents in a week. (b) Perform a goodness of fit test at the 5% significance level of the null hypothesis that the observed number of accidents follow a Poisson distribution. Hint: Use the estimate (to four decimal places) you computed in (a) and report the expected frequency and observed value of the statistic to four decimal places. [ (c) What is the p-value of your test in (b)? Does the p-value indicate that there is evidence against the null hypothesis?
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