• According to a union agreement, the mean income for all senior-level assembly-line workers in a large company equals $500 per week. A representative of a women's group decides to analyze whether the mean income for female employees matches this norm. For a random sample of nine female employees, Y¯=410Y¯=410 and sY=90sY=90.
  
  a. Conduct a hypothesis test of whether the mean income of female employees differs from $500 per week. Include all assumptions, the hypotheses, test statistic, and p-value, and interpret the result. If you need to make an assumption to conduct a test, state the assumption, and conduct the test.
  
  b. Give the 95% confidence interval for the mean income of female employees. Interpret the result.
  
  c. Do these sets of data suggest that the company is guilty of gender discrimination in its compensation policies? Explain.
• 3.2 Suppose you were attending a university where students hated the bookstore and their aggressively high prices. Suppose further that a student organization goes to the bookstore and argues that prices of text books are exceeding $150 per class. At such outrageous prices, students can no longer afford to go to school. The college bookstore claims that an average student pays $101.75 per class for texts (far below the stated claim of $150). A student group randomly selects ten courses from the catalog and finds the costs for each: $140, $125, $150, $124, $143, $170, $125, $94, $127, and $53.
  
  a. Is the sample randomly selected by the students enough to justify the claim that the bookstore is underestimating the amount spent? Why? [Note: So far, on this problem, there is no indication about what kind of statistical analysis you should perform to answer the question. This is often the way that questions appear on assignments and, particularly, the exams. Part of this problem is figuring out what kind of statistical analysis you should perform, and performing it correctly and completely. Previous question prompts have outlined the steps you take for a complete analysis. Make sure that you show your work.]
  
  b. Students decide to take a sample from one more class and find that this class has a textbook cost of $110. Does adding this observation to the other 10 observations change your answer to part (a) above? Why? [Again, this question is prompting you to conduct a statistical analysis, not just answer "yes" or "no".]