An investigator plans to study whether the drug heparin can be used to reduce bronchoconstriction. The investigator wants to determine if taking the drug will increase forced vital capacity (FVC) in the population of individuals with a history of exercise-induced asthma, so a one-sided test will be conducted at the 0.05 significance level.

Amongst the population of those with exercise-induced asthma, the distribution of FVC is approximately normal with mean 3.54 L and known standard deviation of 0.5 L. You can assume the standard deviation for those receiving heparin is the same.

1. State the null and alternative hypotheses of interest.

2.Based on a sample of size 40 patients receiving heparin, what is the probability that the investigator will get a sample mean of 3.61 L or greater if the null hypothesis is true?

3.If the true alternative mean is 3.76 L, what is the power of the test?

4.What is the probability that the investigator will get a sample mean of 3.61 L or less if the alternative mean of 3.76 L is true?

5.Suppose the alternative mean of 3.76 L is true, but the investigator gets a sample mean of 3.61 L. What is her conclusion? What type of error is she making?

6.What is the investigator's chance of making this type of error?

7.If the investigator is willing to have a 10% chance of failing to detect the alternative of 3.76L, what sample size can be used?