A car model breaks down on average 1.5 times a year. The company has developed a fix that claims to have reduced the issue. Alby randomly selects ten cars of the new model and finds eight of them break down in the first year. Did the fix work? Use a significance level (alpha) of 5%.
Since the subject represents counts (car breakdowns) that occur at random, we will use the Poisson Hypothesis testing here.
The null hypothesis, H0 = the average failure rate (lambda) of the new car = 1.5 (same as old)
The alternate hypothesis, HA = the average failure rate (lambda) of the new car < 1.5 (failure reduced)
The R code has the following format: poisson.test(total count, duration, hypothesized rate, region of the alternative)
poisson.test(8, 10, 1.5, alternative = "less") Exact Poisson test
data: 8 time base: 10
number of events = 8, time base = 10, p-value = 0.03745
alternative hypothesis: true event rate is less than 1.5
95 percent confidence interval:
0.000000 1.443465
sample estimates:
event rate
0.8 Since we used the p-value as the criterion and it is less than the significance level (0.05), we reject the null hypothesis in favour of the notion that the fault has been reduced.
Reference
Hypothesis Testing with the Poisson Distribution
