IB Mathematics Applications & Interpretation Question Type 6: Performing a Hypothesis Test on Population Mean Using the Poisson Distribution Exercises

A website experiences on average 1 error per 50 visits. After a patch is applied, 200 visits yield 2 errors. Using a 1% significance level, test if the error rate has decreased.

A factory produces shampoo with an average of 4 faulty products per 200 items. After installing a new machine, a sample of 400 items yields 2 faulty items. At the 5% significance level, test whether the new machine has reduced the fault rate.

A production line averages 3 defects per 100 units. A process change is applied and in the next 200 units there are 4 defects. Test at the 5% level whether the defect rate has increased.

Typographical errors occur at a rate of 20 per 100 pages. After editing, in the next 100 pages there are 15 errors. Test at the 5% level if the error rate has decreased.

A research lab records an average of 3 particle detections per hour. In a 5-hour run, no particles are detected. At the 5% level, test whether the detection rate has changed (two-sided).

A factory reports an average of 6 faulty items per 500-unit batch. Following a process improvement, a batch of 1000 units is found to contain 8 faulty items.

At the 5% significance level, test whether the fault rate has decreased.

A sensor records on average 0.5 events per minute. During a 120-minute period, it records 50 events. At the 5% significance level, test if there is evidence that the event rate has decreased.

A call center receives on average 10 calls per hour. After staffing changes, 36 calls are received in 4 hours. At the 5% significance level, test if the average call rate has changed (two-sided).

A call center logs on average 2 misrouted calls per day. After training, over a period of 30 days, there are 45 misrouted calls. At the 5% significance level, test if the rate of misrouted calls has increased.

A hospital averages 5 emergency admissions per hour. After a policy change, 3 consecutive hours have a total of 20 admissions. Test at the 5% level whether the admission rate has increased.

At a bus stop, arrivals follow a Poisson process with mean 12 per hour. Over a 2-hour period, 18 arrivals are observed.

At the 10% significance level, test whether the arrival rate has decreased.

A quality control process yields an average of 2 defects per 1000 items. A sample of 5000 items has 15 defects. At the 5% significance level, test whether the defect rate has decreased.