MNET 315: INDUSTRIAL STATISTICS

DEPARTMENT OF ENGINEERING TECHNOLOGY

NEW JERSEY INSTITUTE OF TECHNOLOGY

TEST # 1: February 27, 2003

 

1.      A pharmaceutical company runs a clinical study to test three new compounds against a currently used drug for the treatment of congestive heart failure.  Twelve different patients are assigned at random to each of the four compounds, treated, and measured for the effectiveness of the compound.

What is the sample and what is the population of interest?  Is it a survey or experimental study? 

 

Sample: Randomly selected 12 patients

Population of interest: All congestive heart failure patients.

It is an experimental study, because it is actively changing the condition of the sample.

 

2.      In 2001, major league baseball teams spent a total of $1,968,088,814 on player salaries.  Does this numerical value describe a population parameter or a sample statistics?

Population parameter - because it is a numerical figure pertaining to the whole base ball player population.

 

3.      “Pie and bar charts are useful for describing categorical (nominal) data, while histograms and stem plots are useful for describing quantitative data” True or False?

 

4.      Numerical measure of central tendency of a measured data set can be (select the correct one)

  1. Mode
  2. Median
  3. Arithmetic mean
  4. Trimmed mean
  5. All of the above

 

5.       “There cannot be more than one mode in the data set” True or False?

 

6.      “Median is the central value of a data set: 50% of measurements in the data set lie above it, and 50% fall below it.” True or False?

 

7.      “Median is influenced by the extreme values in the data set” True or False?

 

8.      “Arithmetic mean is obtained by averaging all measurements in a data set and hence its value is influenced by the extreme measurements.” True or False?

 

9.      "Interquartile range (IQR) is a measure of __variability__  of a data set."

 

10.  "If a data set is skewed to the right, the mean is expected to be larger than the median." True or False?


 

11.  Following are the number of home runs that Babe Ruth hit in each of his 15 years with the New York Yankees, 1920 to 1934.

54  59  35  41  46  25  47  60  54  46  49  46  41  34  22

a.       Draw a stem and leaf plot.  Then find the five descriptive measures - Median, Q1, Q3, the smallest and the largest value and draw the box and whisker plot.

 

b.      If  659 and  1770.933, them find the find the mean and standard deviation of the home runs.

 

 

a. Stem and leaf plot:

2

2

5

 

 

 

 

 

3

4

5

 

 

 

 

 

4

1

1

6

6

6

7

9

5

4

4

9

 

 

 

 

6

0

 

 

 

 

 

 

 

There are 15 measurements hence the middle one is (15+1)/2 = 8. Thus the median is the 8th measurement, when the data is ordered. From leaf and stem plot the median = 46.

 

Q1 is the median of the first half of the data, i.e the 4th one, and Q3 is the median of the second half of the data, i.e. the 12th one.  Thus the five number summary is: Min.=22, Q1=35, Median = 46, Q3 = 54, and Max. = 60

 

 The box and whisker plot is as follows:

  

 

 

 

 

 

 

 

12.  A data processing company requires applicants for computer programming positions to take a test.  The company policy is to reject all applicants whose score is below 50.  The mean score of the applicants has been 60 with standard deviation of 10.  The distribution of the applicants' scores is mound shaped. Approximately what percentage of applicants has been rejected by the test?

 

 

 

 

 

 

 

If the distribution is mound shaped then we know from the empirical rule that roughly 68 percent of all measurements should lie within + or - one standard deviation from the mean of the measurements.  The score 50 is one standard deviation away from the mean score of 60. As the distribution is also symmetrical, the roughly 16% of the applicants will get score below 50, and thus be rejected.

 

13.  Consider the following outcomes for an experiment

 

Outcome          1          2          3          4          5

Probability        .20       .25       .15       .10       .30

 

Let event A consists of outcomes 1, 3 and 5, and let event B consists of outcomes 4 and 5

a.       Find P(A) and P(B)

b.      Find P(A|B)

c.       Are events A and B mutually exclusive? Give reason supporting your answer

d.      Are events A and B independent to each other? Give reason supporting your answer.

 

 

  1. P(A) = P(1)+P(3)+P(5) = 0.20 + 0.15 + 0.30 = 0.65

P(B) = P(4)+P(5) = 0.10 +0.30 = 0.40

 

  1. P(A|B) = P(AÇB)/P(B) = 0.30/0.40 = 0.75
  2. Not mutually exclusive, because the outcome 5 will cause both event A and B to happen.
  3. Not independent either, because P(A) ¹ P(A|B)

 

 

 

 

 

14.  Forty percent households in the United States own a computer.  You randomly select six households and ask if they own a computer.  What is the probability that:

a.       Exactly two of them will respond yes

b.      At least two of them will respond yes

 

It is a binomial distribution problem, with p = 0.4, and n = 6, thus reading the probabilities for the binomial table

 

a.       P(y = 2)6 = 0.3110

b.      P(y ³2)6 =  P(y = 2)6 + P(y = 3)6 + P(y = 4)6 +  P(y = 5)6 + P(y = 6)6

= 0.3110 + 0.2765 + 0.1382 + 0.0369 + 0.0041

= 0.7667

Alternatively, P(y ³2)6 =  1- [P(y = 0)6 + P(y = 1)6] = 1-[0.0467+0.1866] = 0.7667