IBDP Tutor - Maths AI Type I and II Error (statistics) c. Find the probability of a Type II error.

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IBDP Tutor - Maths AI Type I and II Error

The number of fish that can be caught in one hour from a particular lake can be modelled by a Poisson distribution.

The owner of the lake, Emily, states in her advertising that the average number of fish caught in an hour in three.

Tom, a keen fisherman, is not convinced and thinks it is less than three. He decides to set up the following test. Tom will fish for one hour and if he catches fewer than two fish, he will reject Emily's claim.

a. State a suitable null and alternative hypothesis for Tom's test.

b. Find the probability of a Type I error.

c. The average number of fish caught in an hour is actually 2.5.
*Find the probability of a Type II error.*