Question

Randomly selected deaths of motorcycle riders for the last four months of last year are summarized in the table below (based on data from the Insurance Institute for Highway Safety). Conduct a hypothesis test wit a 5% significance level that such fatalities do not occur with equal frequency during the last four months of last year. a) perform a validity check (5 points) b) state the null and alternative hypotheses (10 points) c) report the chi-square value and p-Falue (10 points) d) provide a non-statistical conclusion (10 points) Month Frequency September 28 October 14 November 10 December 8

Answer 1

a) The chi-square goodness of fit test is appropriate when

1. The sampling method is simple random sampling.
2. The variable is categorical.
3. number of sample observations in each level of the variable is at least 5.

b) H0: fatalities occur with equal frequency i.e. 60/4 = 15

Ha: fatalities do not occur with equal frequency.

c)

Observed Expected Chi-Square Component Categories O; Ei (0;-E;)2 / E; Category 1 28 15 11.2667 Category 2 14 15 0.0667 Category 3 10 15 1.6667 Category 4 8 15 3.2667 Total: 60 60 16.2668

P-value: 0.001

p value is less than given significance level 0.05 so we have to reject null hypothesis

d) .it means there is sufficient evidence to conclude that fertility is do not occur with same frequency.

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