Consider a random sample of 5 adults over the age of 25 from a large population, which is normally distributed, where E represents the total years of education completed: ? = {9,12,14,16,19} Suppose that someone claims that the average person in the population has completed 18 years of education (? = 18 ). A. What is the null hypothesis? What is the alternative hypothesis? B. Can you reject the null hypothesis at the 10?percent level of significance? Can you reject the null hypothesis at the 5?percent level of significance? Use the critical value approach. You can use R for critical values, but you must show all of your calculations and explain. Use R, however, to check your work. C. What is the 95?percent confidence interval for years of education? Use the 95?percent confidence interval to conduct the test in Part B using the 5? percent level of significance. Provide a written interpretation explaining your answer.

Consider a random sample of 12 construction workers, six of whom belong to a labor union and six of whom do not. The hourly wages for each worker are reported below: Wages of union members Wages of non-union members 18 25 30 20 40 34 35 30 26 20 25 15 A. Test whether the population variance of one group is greater than the population variance of the other group using an F test. Test at the 5-percent level of sigjucance? What is the value of you: test statistic and what is the critical value? 1Li'llhat can you conclude and why? Test whether union members in the population have higher wages than nonunion members using a ttest. 'What are the null and alternative hypotheses? "Nl'uch version of the ttest should you use and why? 1What can you conclude at the lpercent level of significance? Explain