Math 203, Introduction to Statistics,
Central College, Spring 2000 Exam 3 Review Sheet.
The answers
  1. A manufacturer of PVC irrigation pipes claims that the mean bursting pressure of their pipes is 425 psi (pounds per square inch). A consumer watchdog group fears that the bursting pressure may be lower and tests a random sample of 10 such pipes. The bursting pressures are listed below.
401 359 383 427 414 415 389 463 394 428
    1. Define the null and alternative hypothesis for a significance test to help decide if the bursting pressure is lower than claimed by the manufacturer.
    2. Carry out the test described in part (a) and report the p-value of this test.
    3. Explain in common language what this p-value tells you.
    4. Do you think that the watchdog group has a legitimate fear?
    5. Based on the sample above, give a 95% confidence interval for the mean bursting pressure of this type of PVC pipe.

      6.  
  1. An agricultural researcher reasons as follows: A heavy application of potassium fertilizer to grasslands in the spring seems to cause lush early growth but depletes the potassium before the growing season ends. Spreading the same amount of potassium over the growing season might increase yields. He therefore compares two treatments:
      2. treatment 1: 100 lbs per acre in the spring;
      treatment 2: 50, 25 and 25 pounds per acre applied in spring, early summer and late summer.
    The experiment is continued over several years because grass yields vary greatly from year to year. The yields (in pounds of dry matter per acre) are known to vary roughly with a normal distribution (over all years). The data observed in the experiment are given below.
     
    Treatment year 1 year 2 year 3 year 4 year 5
    1 3902 4281 5135 5350 5746
    2 3970 4271 5440 5490 6028
      1. Why is a one sample test appropriate here?
      2. Do the data give good evidence that treatment 2 leads to higher average yields? Fully describe the test you use to answer this question.
      3. Give a 98% confidence interval for the mean increase in yield due to spreading the potassium applications over the growing season.
  2. The store manager of the local grocery store claims that customer complaints vary normally from week to week with a mean of 13 complaints per week and a standard deviation of 3 complaints per week. After hiring several new checkout clerks, the manager is worried that the average number of complaints per week has increased. The manager decides to test this hypothesis at the 5% level by selecting a random sample of 10 weeks and calculating  = the average number of complaints for these 10 weeks. If the average number of complaints is too high (significant at the 5% level), the manager will fire the new checkers.
    1. Define the null and alternative hypothesis and sketch a (well labeled) normal density curve that illustrates the rejection interval (the values of  that will cause the manager to fire the checkers).

      2.  

       
       
       
       
       
       

    2. Several possible results from the test above are stated below. In each case, decide if the checkers are fired or not fired.
      1. The p-value of the test is 0.09.
      2. The p-value of the test is 0.02.
      3. The test yields  = 14.56.
      4. The test yields  = 13.29.
      5. The test yields  = 15.71.
    3. Write down the acceptance interval (the values of  that allow the newly hired checkers to continue working).
    4. Describe in common words what a type I error means in this case, and what a type II error means in this case.
    5. What is the probability of a type II error if m = 15.5? What is the power of this test against the alternative m = 15.5?
  3. Monthly salaries (in dollars) of recent graduates with a statistics course are known to vary normally with a standard deviation of $323 per month. You would like to estimate the mean monthly salary of all such graduates with a 90% confidence interval and a margin of error of $150. How large should your sample be?

    4.  
  4. Which of the following data sets are safe for using T-procedures? For the ones that are not safe, explain why they are not safe. For the ones that are safe, calculate , SX, and a 95% confidence interval for the population mean.
    1. A random sample of size 142 is selected from a population that is significantly skewed to the right.
    2. The data are: 80,22,17,131,-19,3,23,-1,20,-51,-3
    3. The data are: 11,18,1,4,6,19,6,3,13,1,-1

      4.  
  5. Two experimental diets (diet 1 and diet 2) designed to add weight to malnourished 3rd world children are fed to independent and random samples of such children. The results in weight gains are summarized in the table below. Do the data support the claim that diet 2 adds significantly more weight than diet 1? Fully describe and carry out the test you use to make this decision.
Diet 1 Diet 2
1 = 5.80 pounds 2 = 7.27 pounds
 n1 = 8  n2 = 9
 S1 = 1.613 pounds  S2 = 0.99 pounds