Testing a Poisson mean Problem set A

For each test, X ~ Po(λ). Find the p-value and state the conclusion.

1. (a) H0: λ = 12, H1: λ < 12, significance level 5%, observed value x = 8.
2. (b) H0: λ = 7.5, H1: λ < 7.5, significance level 5%, observed value x = 3.

For each test, X ~ Po(λ). Find the p-value and state the conclusion.

1. (a) H0: λ = 4, H1: λ > 4, significance level 5%, observed value x = 9.
2. (b) H0: λ = 10, H1: λ > 10, significance level 10%, observed value x = 15.

Find the critical region for each test.

1. (a) X ~ Po(λ), H0: λ = 12, H1: λ < 12, significance level 5%.
2. (b) X ~ Po(λ), H0: λ = 8.2, H1: λ < 8.2, significance level 10%.

Find the critical region for each test.

1. (a) X ~ Po(λ), H0: λ = 7.5, H1: λ > 7.5, significance level 5%.
2. (b) X ~ Po(λ), H0: λ = 1.8, H1: λ > 1.8, significance level 2%.

A customer service desk has averaged 4.2 complaints per day. After staff training, the manager thinks the average rate has decreased. Over the next 5 days there are 14 complaints. Test her belief at the 5% significance level.

1. (a) Write down hypotheses, defining λ and X.
2. (b) Find the p-value.
3. (c) State the conclusion in context.

A hospital emergency department has averaged 3.2 arrivals with sports injuries per hour on Saturdays. After a tournament starts nearby, a nurse thinks the average rate has increased. In a 2-hour period there are 11 such arrivals. Test her belief at the 5% significance level.

1. (a) Write down hypotheses, defining λ and X.
2. (b) Find the p-value.
3. (c) State the conclusion in context.

An astronomer sees an average of 11 meteors per night from her garden. After a new street lamp is fitted, she thinks the average rate has decreased. She counts the meteors on one night. Use a 5% significance level.

1. (a) Define X and write down hypotheses.
2. (b) Find the critical region.
3. (c) There are 4 meteors. State the conclusion.

Find the critical region for each binomial test.

1. (a) X ~ B(60, p), H0: p = 0.15, H1: p > 0.15, significance level 5%.
2. (b) X ~ B(40, p), H0: p = 0.2, H1: p > 0.2, significance level 10%.

A helpline has averaged 2.4 calls per hour. The manager thinks the average rate has increased since a new advertisement. She counts the calls over a 5-hour period and tests at the 5% significance level.

1. (a) State two conditions that must hold for the Poisson distribution to be a suitable model.
2. (b) Write down hypotheses and find the critical region for the number of calls in 5 hours.
3. (c) There are 19 calls in the 5 hours. State the conclusion in context.