Reading Questions 17b

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Problem 1. 

Data is drawn from a normal distribution with unknown mean μ. We make the following hypotheses:

H0: μ=1   and   HA: μ>1.

(a) Is H0 a simple or composite hypothesis?

 Simple
 Composite
  

(b) Is HA a simple or composite hypothesis?

 Simple
 Composite
  

(c) Is HA a one or two-sided?

 One-sided
 Two-sided
  

Problem 2. 

We want to estimate the value of an unknown variance σ2. The null hypothesis H0 is that σ2=1. Of course we know that σ2>0. Other than that we only care whether or not σ2 is 1. Should we have a one or two-sided alternate hypothesis?

 One-sided
 Two-sided
  

Problem 3. 

Our data is normal with variance 25. The null hypothesis is that the data is drawn from N(10, 25). That is, the null distribution has μ=10. We have 1 data point x=20.

(a) If the alternative hypothesis is one-sided μ>10. What is the p-value for this data?
 

(b) Suppose our significance level is 0.05. Will we reject the null hypothesis?

 Yes
 No