Exercises. 1. Find the p-value for each of the following hypothesis tests

1. Find the p- value for each of the following hypothesis tests

a) ; ; ; ; ;

b) ; ; ; ; ;

c) ; ; ; ;

2. Consider ; against the alternative .

A random sample of 60 observations taken from this population produced a sample mean of 31.4 and a standard deviation of 8.

a) Calculate the p- value.

b) Considering the p- value of part a), would you reject the null hypothesis if the test were made at the significance level of 0.05?

c) Considering the p- value of part a), would you reject the null hypothesis if the test were made at the significance level of 0.01?

3. In a given situation, suppose was rejected at . Answer the following questions as “yes”, “no”, or “can’t tell” as the case may be.

a) Would also be rejected at ?

b) Would also be rejected at

c) Is the p- value smaller than 0.05?

4. In a problem of testing against , the following sample quantities are recorded.

a) State the test statistic and find the rejection region with .

b) Calculate the test statistic and draw a conclusion with .

c) Find the p- value and interpret the results.

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