Exercises. 1. Make the following tests of hypotheses.

1. Make the following tests of hypotheses.

a) ; ; ; ; ;

b) ; ; ; ; ;

c) ; ; ; ; ;

2. Consider ; against the two sided alternative .

a) A random sample of 64 observations produced a sample mean of 98 and a standard deviation of 12. Using , would you reject the null hypothesis?

b) Another random sample of 64 observations taken from the same population produced a sample mean of 104 and a standard deviation of 10. Using , would you reject the null hypothesis?

Comment on the results of parts a) and b).

3. A survey showed that people with a bachelor’s degree earned average of $2116 a year in 2001. A sample of 900 persons with a bachelor’s degree taken recently by a researcher showed that the persons in this sample earned on average of $2345 a year with a standard deviation of $210. Test at 5% significance level whether people with a bachelor’s degree currently earn an average of $2116 against the alternative that it is more than $2116 in a year.

4. The manufacturer of a certain brand of auto batteries claims that the mean life of these batteries is 45 month. A consumer protection agency that wants to check this claim took a random sample of 36 such batteries and found the mean life for this sample is 43.75 month with a standard deviation of 4 month. Using the 2.5% significance level, test the manufacturer claim against the alternative that the mean life of batteries is less than 45 month.

5. A random sample of 100 observations from a population with standard deviation 60 yielded a sample mean of 110.

a) Test the null hypothesis that against the alternative hypothesis that using . Interpret the results of the test.

b) Test the null hypothesis that against the alternative hypothesis that using . Interpret the results of the test.

c) Compare the results of the two tests you conducted. Explain why the results differ.

6. In a random sample of 250 observations, the mean and standard deviation are found to be 169.8 and 31.6, respectively. Is the claim that larger than 169 substantiated by these data at the 10% level of significance?

7. From records, it is known that the duration of treating a disease by a standard therapy has a mean of 15 days. It is claimed that a new therapy can reduce the treatment time. To test this claim, the new therapy is tried on 70 patients, and from the data of their times to recovery, the sample mean and standard deviation are found to be 14.6 and 3.0 days, respectively.

Perform the hypothesis test using a 2.5% level of significance.

8. Suppose that you are to verify the claim that on the basis of a random sample of size 70, and you know that .

a) If you set the rejection region to be , what is the level of significance of your test?

b) Find the numerical value of c so that the test has a 5% level of significance.

Дата добавления: 2015-08-05