Fall 2008 Statistics Venable TEST 3 PRACTICE TEST 3

Please show all work - even work done by calculator. Please show all steps in hypothesis test and p-value problems.

  1. A sample of 400 workers selected from California showed that they earn an average of $685 per week. The population standard deviation is known to be $125. Construct a 95% confidence interval for the mean weekly earnings of all workers in California.
  1. A manager of a driving school claims that the mean time taken to learn how to drivea car is 8.0 hours for all new drivers. A sample of 16 new drivers showed that the meantime taken by them to learn how to drive a car is 9.5 hours with a population standard deviation of1.607 hours. Find the p-value for the test that the mean time taken to learn how to drive acar is greater than 8.0 hours.Assume that the population from which the sample is drawn is normally distributed.
  1. In a poll of 1500 adults, 450 adults said that they live a stressful life. Construct a99% confidence interval for the proportion of all adults who live a stressful life.
  1. A researcher wants to estimate the mean income of all physicians in the city at a95% confidence level. The standard deviation of the incomes of all physicians in this cityis $17,500. What sample size is required to obtain an estimate that is within $5000 of thepopulation mean?
  1. A department store claims that at least 45% of persons who visit this store make apurchase. In a sample of 400 persons whovisited this store, 37% made a purchase. Test atthe 5% significance level if the claim of the management is true.
  1. A sample of 1000 persons showed that 24% of them own stocks. Construct a 95%confidence interval for the proportion of all persons who own stocks.
  1. In 1990, the mean cost of a hotel room in the United States was $125 per day. Arecent sample of 25 hotels showed that the mean cost of a hotel roon1 is $138 per day witha standard deviation of $26. Test at the 2.5% significance level if the current mean cost of ahotel room is higher than $125.Assume that the population from which the sample is drawn is normally distributed.
  1. A random sample of 28 students selected from a middle school showed that theyspend an average of 45 minutes on homework per day with a standard deviation of 10minutes. Assume that the time spent on homework per day by all students at this schoolhave an approximate normal distribution. Construct a 90% confidence interval for the mean time spent on homework per day by all students at this school.
  1. A researcher claims that the starting mean salary for new college graduates is$26,700. A sample 'of 100 recent college graduates showed that their mean starting salaryis$28,200. The population standard deviation is $2700. Test at the 5% significance level if the mean starting salary of new college graduates is different from $26,700.
  1. The mean price of all college text books was $102 in 2006. The population standarddeviation is known to be $11. A sample of 34 college textbooks take this year gave a meanprice of $107. Find the p-value for the test that the current mean price of all textbooks isgreater than $102.