In a crossover trial comparing a new drug to a standard, π denotes the probability that the new one is judged better. It is desired to estimate π and test H0 : π = 0.5 against H1 : π =/= 0.5. In 20 independent observations, the new drug is better each time.

(a) Find and PLOT the likelihood function, but I know it's. Give the ML estimate of π.

(d) Suppose that researchers wanted a sufficiently large sample to estimate the probability of preferring the new drug to within 0.05, with confidence 0.95 (i.e., the 95% confidence interval is of length 0.1), If the true probability is 0.80, about how large a sample is needed based on Wald type confidence interval?

In a crossover trial comparing a new drug to a standard, π denotes the probability that the new one is judged better. It is desired to estimate π and test H0 : π = 0.5 against H1 : π =/= 0.5. In 20 independent observations, the new drug is better each time.

(a) Find and PLOT the likelihood function, but I know it's. Give the ML estimate of π.

(d) Suppose that researchers wanted a sufficiently large sample to estimate the probability of preferring the new drug to within 0.05, with confidence 0.95 (i.e., the 95% confidence interval is of length 0.1), If the true probability is 0.80, about how large a sample is needed based on Wald type confidence interval?

A firm is considering two projects, A and B, with the following probability distributions for profit.

Profit ($1,000s). Project A Probability (%)   Project B Probability (%)   

$20 10 10

40 15 15

60 50 25

80 15 40

100 10 10

a. Compute the expected value of project A (in $1,000s).

b. Compute the variance of project A (in $1000s).

c. Compute the expected value of project B (in $1000s).

d. Which project would be selected if an analysis of variance rule were applied?

e. Which project would a risk-neutral manager select?

f. Report the coefficients of variation (?

the probability that a worker with occupational exposure to dust contracts a lung disease is 0.2. three such workers are checked at random. find the probability that

a. none of the three workers contracted a lung disease.

b. at least one of them contracted a lung disease

What is the probability that a randomly selected member of a normally distributed population will lie more than 1.8 standard deviations from the mean?

e) T F The larger the sample that is taken, the probability of making a type 2 error increases.

f) T F We can never conclude that H0 is true based on taking a random sample from from the population.

g) T F A stratified random sample is more preferred over a simple random sample when the population can be divided into homogeneous groups.

Find the probability that the sample mean is less than 984 if a sample of size 100 is taken from a population with a mean of 1000 and a standard deviation of 300.

A group of twenty-seven people is selected at random. What is the probability that at least two of them will have the same birthday? (Round your answer to four decimal places.)

The life time of a dryer machine can be modeled with the probability distribution , where x is the time in years and beta is an unknown parameter. Findings that 3 machines life time are after x₁, x₂, x₃ years.

1. what is the likelihood function?

2. assume the observations are x₁ = 5, x₂ = 6, x₃ = 5. Use this information and simplify the likelihood function as much as possible.

3. what is the log-likelihood function, simplified as much as possible for beta?

4. what is the maximum likelihood estimate for beta, use two decimal places?

What is the probability that a randomly selected composition of N that has a second part equal to 1?