Transport engineers are interested to study the pattern Question 4 and the risk of accidents at a junction. Suppose we observe the following frequency distribution of the number of accidents in 150 weeks. Number of Accidents 0. 1 3 4. 6. 7+ Observed frequency 50 30 24 30 10 (Y Find an estimate (to four decimal places) of the average number of accidents in a week. 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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Question 4
and the risk of accidents at a junction. Suppose we observe the following frequency
distribution of the number of accidents in 150 weeks.
Transport engineers are interested to study the pattern
Number of Accidents
0.
1
3
4.
7+
Observed frequency
50
30
24
30
10 5
1
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:Question 4 and the risk of accidents at a junction. Suppose we observe the following frequency distribution of the number of accidents in 150 weeks. Transport engineers are interested to study the pattern Number of Accidents 0. 1 3 4. 7+ Observed frequency 50 30 24 30 10 5 1 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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