Question

It is known that a group of people is susceptible to a disease according to a binomial process. Ten people are observed—let X denote the number who are found to be susceptible. We would like to distinguish between the possible cases pi = 10% and pi = 20%.   Using Excel:

If four people are found to be susceptible, which is the more likely value of pi?

Find a decision rule for distinguishing between the two values of pi based on a sample of 10.

If possible please include excel functions used. thank you

Answer 1

Answer: Given,

In cases pi =10% and pi =20%

sample = 10

Here, the distribution given to us is:

Now for = 0.1, we compute P(X = 4) as:

Now for = 0.2, we compute P(X = 4) as:

Now as probability of X = 4 is more for = 0.2 than for = 0.1, therefore = 0.2 is more likely value of