# Activity 04/30/21

## Student Name:

## Instructions:
Fill in your name above.  We will work through the following activities as a group in the discussion sections.  You must turn in a completed worksheet with solutions filled in below for credit.  The solutions will be given in the discussion section.


## Activity: General hypothesis testing, power of tests and sample sizes

### Question 1:

Cloud seeding has been studied for many decades as a weather modification procedure (for an interesting study of this subject, see the article in Technometrics, "A Bayesian Analysis of a Multiplicative Treatment Effect in Weather Modification", Vol. 17, pp. 161–166). The rainfall in acre-feet from 20 clouds that were selected at random and seeded with silver nitrate follows:

```{r}
rainfall <- c(18.0, 30.7, 19.8, 27.1, 22.3, 18.8, 31.8, 23.4, 21.2, 27.9, 31.9, 27.1, 25.0, 24.7, 26.9, 21.8, 29.2, 34.8, 26.7, 31.6)
```


Can you support a claim that mean rainfall from seeded clouds exceeds 25 acre-feet? Use $\alpha = 0.01$ significance.


### Question 2:

Compute the power of the test if the true mean rainfall is 27 acre-feet.



### Question 3:

What sample size would be required to detect a true mean rainfall of 27.5 acre-feet if we wanted the power of the test to be at least 0.9?

