Probstat/homework 3

This is part of probstat.

Part 2: Hypothesis testing

1. We are interested in testing if a normally-distributed population has mean zero. We know that the variance of the population is 17. If we decide to take a sample of size 15, design a hypothesis testing procedure with the level of significance $\alpha =5\%$. State the null hypothesis clearly and describe the criteria for accepting/rejecting the null hypothesis.

2. We are interested in testing if a normally-distributed population has mean at least 100. We know that the variance of the population is 30. If we decide to take a sample of size 10, design a hypothesis testing procedure with the level of significance $\alpha =5\%$. State the null hypothesis clearly and describe the criteria for accepting/rejecting the null hypothesis.

3. We are interested in testing if a normally-distributed population has mean at least 100. However, we do not know the population variance. If we decide to take a sample of size 10 to compute the sample mean ${\bar {X}}$ and the sample variance $S^{2}$, design a hypothesis testing procedure with the level of significance $\alpha =10\%$. State the null hypothesis clearly and describe the criteria for accepting/rejecting the null hypothesis.