Math 135 Extra Credit

For each question that is COMPLETELY correct, the listed number of points will be added to either test 1 or test 2. All points must be added to either one test or the other. Under no circumstances will I assign a grade higher than 105 on any particular test. While you may work with classmates on this assignment, no LAC help/outside tutor help is to be given. You may also ask questions of your instructor.

Neatness counts! Work should be organized, written on looseleaf paper with all StatCrunch output attached (all pages should be stapled together). Work that is submitted that does not meet this criteria will not be graded.

Due: Friday, November 15 (NO EXCEPTIONS!!! This is BONUS work!)

Assign points to (circle one) TEST 1 TEST 2

  1. (2 points) Rollflex and Morgan Trust are two stocks traded on the New York Stock Exchange. For the past seven weeks you recorded the Friday closing prices for each as follows:

Rollflex 51 48 49 53 49 49 50
Morgan Trust 53 51 46 50 50 58 54
  1. Compute the mean and median for each (by hand)
  2. Compute the 5 # summary for each (by hand)
  3. Compute the standard deviation for each (using StatCrunch)
  4. Construct side by side box plots to compare the two stocks using StatCrunch.
  5. Based on your statistics and graph, can you conclude that one stock generally gives a higher return than the other? Which stock would be considered more stable?
  1. (2 points) A random sample of 25 orders at a fast-food restaurant was selected and the dollar amount for each was recorded (rounded to the nearest dollar). The results were as follows:

12 33 18 13 15 2 23 17 9 11 5 7 12 16 25 29
4 23 7 3 27 14 14 9 6
  1. Construct an appropriate graph to determine the shape for the dollar amount spent.
  2. Describe the shape and give appropriate measures for center and spread.
  3. Can you assume that your data are roughly Normal? Construct an appropriate graph (using StatCrunch) to check for normality. Defend your answer.
  4. If you were to assume that the population is normal, what significance test would you use to test to see if the true average amount spent for this restaurant is greater than $15? Explain.
  1. (1 point) An SRS of 50 patients is selected from a local blood bank. The distribution of blood types were found to be the following:

Blood Type / O / A / AB / B
Count / 34 / 12 / 1 / 3
  1. What is the variable of interest here? Identify the variable as categorical or quantitative.
  2. Construct an appropriate graph to display this variable.
  3. Summarize your results (describe the graph).

  1. (2 points)*An efficiency expert developed a test measuring job satisfaction of civil service clerks. An SRS of 10 clerks was selected and the following information was obtained:

Job satisfaction / 92 / 32 / 56 / 20 / 72 / 16 / 56 / 76 / 80 / 48
Days absent from work (in one year) / 8 / 14 / 10 / 14 / 6 / 17 / 8 / 12 / 7 / 15
  1. What type of relationship is being investigated here? (i.e. QQ, CQ, CC).
  2. Treating job satisfaction as your explanatory variable, construct an appropriate graph to determine whether a relationship appears to exist.
  3. Describe the graph in terms of form, direction and strength.
  4. Compute the correlation. Compute the least squares regression line and list the equation.
  5. Interpret what the slope represents in the context of the data.
  6. Use the regression equation to predict the number of days absent based on a job satisfaction score of 60.
  7. Construct a residual plot. Is there a pattern? What does this indicate?

*Use of StatCrunch is appropriate for the graphs and computations in this problem.

  1. (2 points) The Army gives a battery of exams to all new recruits. One exam measures a person’s ability to work with technical machinery. This exam was given to a random sample of 360 recruits. The results are shown in the table below where x is the score on a 10 point scale and F is the frequency of new recruits with this score.

X / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
F / 28 / 42 / 79 / 83 / 51 / 36 / 18 / 12 / 7 / 4
Probability, P(X)
  1. Find the probability distribution for random variable X.
  2. Is X discrete or continuous? Explain.
  3. Construct a probability histogram for X. Describe the histogram’s shape.
  4. Find P(X > 3). Find P(X ≥ 3).
  5. The kitchen battalion can use people with a score of three or less. Find the probability that a new recruit is not overqualified for kitchen duty.
  1. (1 point) For each of the following probabilities, shade the area under the standard normal curve corresponding to the probability. Then find the requested probability.

a. P(0 < Z < 1.71)b. P(Z < 0.43)

c. P(Z > 0.43)d. P(-3.19 < Z < 2.14)

  1. (1 point) The snow pack on the summit of Wolf Creek Pass, Colorado on March 1 has been measured for many years by the National Weather Bureau. The depth of the snow pack in inches is roughly normally distributed with a mean of 78.1 inches and a standard deviation of 10.4 inches. For a given year, find the probability that the snow pack will be

a. less than 60 inchesb. more than 85 inches

c. between 60 and 85 inches

  1. (2 points) Find the z value such that
  1. 10% of the area of the standard normal curve lies to the right of z.
  2. 80% of the area of the standard normal curve lies between –z and z.
  3. 98% of the area of the standard normal curve lies between –z and z.

(Must show graphs for this problem)

  1. (1 point) The life of the Corn Delight popcorn maker is normally distributed with mean 20 months and standard deviation 2 months. The manufacturer will replace a Corn Delight popper if it breaks during the guarantee period. How long should the guarantee period be if the manufacturer does not want to replace more than 3% of the poppers? (round to the nearest month)
  1. (1 point) The life of one species of poplar tree is normally distributed with mean 20 years and standard deviation 2.3 years.
  1. If one tree is selected at random, what is the probability it will live 21 years or more?
  2. If nine trees are selected at random, what is the probability the sample mean life of the trees will be 21 years or more? Even though the central limit theorem does not apply here, why can we assume that the sample mean will follow a normal distribution?
  1. (1 point) The twister roller coaster is one of the top roller coasters in the nation. There is always a long line of thrill seekers waiting to take a ride. A random sample of 60 riders waited in line for a sample mean time of 40 minutes with a sample standard deviation of 12 minutes. Compute a 90% confidence interval for the true population mean wait time for the Twister coaster. Explain what this confidence interval represents.
  1. (2 points) The Magic Dragon cigarette company claims that their cigarettes contain an average of only 10 mg of tar. A random sample of 100 Magic Dragon cigarettes shows that the average tar content per cigarette to be 11.5 mg with a standard deviation of 4.5 mg. Is this enough evidence to indicate that the true average tar content of Magic Dragon cigarettes exceeds 10 mg? Conduct the appropriate significance test. Use α=0.05. List the assumptions, hypotheses, test statistic, p-value and conclusion.