MTH5102 Pretest A

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MTH-5102 Pretest A

• a) Tania has been submitted to an admission test
  in a program of excellence. Her standard score
  is 3.0 and her mark is 82. The groups standard
  deviation was 11.3.
• What is the arithmetic mean of the group?

b) Complete the following table.

• Marilyn and Carol-ann have passed the same exam
  in 2 different groups. The standard score has
  been calculated for each. As a result,
  Carol-anns standard score is lower than that of
  Marilyn, even if they obtained the same result on
  the exam.
• a) If the mean is the same in the 2 groups, in
  which group do we find the smallest standard
  deviation? (Explain)
• b) If the standard deviation is the same in the
  2 groups, which group shows the lowest mean?
  (Explain)

2

• Before concluding a transaction for the street
  lights of a city, the municipal engineer is doing
  a test on a sample of 12 lights of Brand A and
  Brand B. The life span in hours of the lights
  resulted as follows
• a) Calculate the mean life span and the
  standard deviation of the 2 brands.
• b) If the standard deviation is the same in the
  2 groups, which group shows the lowest mean?
  (Explain)

• The members of a selection committee are
  verifying the files of four candidates for an
  accounting position. The are from the same
  CEGEP but are a part of four different groups.
• In the table below, we indicate the mark of each
  candidate as well as the mean and standard
  deviation of the group they belong to.

In which order will the committee consider the
applications if they first consider the Z-score
of the candidates? Show your work.
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• Each of the graphs below represents the
  correlation between the age of an adult and a
  variable.

Which of the following choices orders these
graphs according to the strongest correlation?
A) Graph 1, graph 2, graph 4, graph 3
B) Graph 1, graph 3, graph 4, graph 2
C) Graph 3, graph 1, graph 2, graph 4
D) Graph 3, graph 1, graph 4, graph 2
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• Match the correlation coefficients to the
  corresponding situations.
• A) A weak correlation exists between the number
  of hours passed in front of a TV set in a week
  and peoples age. We notice a small tendency to
  spend more time in front of the TV among older
  people.
• B) No correlation exists between the number of
  centimeters of snow that falls during a winter
  and the number of centimeters of rain that falls
  during the summer.
• C) A moderate correlation was determined
  between the average number of hours passed to
  study each day and the general average of marks
  on the reports. This correlation indicates a
  certain improvement on the general average when
  the number of hours in study increases.
• 1. r -0.68 2. r -0.45
  3. r 0 4. r 0.45
  5. r 0.68

• The following scatter plot represents the
  relation between the mass and the consumption of
  gas for 15 cars.

Using the rectangle method, estimate coefficient
of linear correlation between the mass and the
gas consumption of the cars.
5

• Specialists have analyzed the relation between
  the health factor of a person and his heartbeat
  recorded during a fairly intensive physical
  activity. The data collected are presented below

a) Using the median-median line method and the
scatter plot, determine an approximation of the
equation of the regression line.
b) According to the linear model obtained, what
would be the health factor of a person whose
heart beat is 75?
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• Magalie is doing research on the amount of fat,
  sodium and cholesterol found in 14 different
  boxes of chocolate cookies.
• She presents the results of her research in the
  following table

From this information, what is the degree of
correlation between the amount of cholesterol and
the amount of sodium contained in these 14
boxes? Justify your answer. A) Moderate and
positive B) Moderate and negative C) Strong
and positive D) Strong and negative
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• The following table shows the IQ, Math mark and
  Music mark for 13 students in a school. Is there
  a correlation between the IQ and either of the
  marks.

• A statistical analysis of the data gives us the
  following results
• Between the IQ and the Math mark r 0.589
• y 0.4826x 89.6
• Between the IQ and the Music mark r 0.2939
• y 0.25x 99.4
• Can we conclude that the marks obtained I Math
  and Music offers a good evelaution of the
  intelligence quotient of a student? Explain.
• If Carl has 48 in Math and 62 in Music, which
  model will he choose to obtain the best IQ.

8

• A hockey player wants to know if theres a link
  between the number of minutes of ice-time and the
  number of points that he achieved. The table
  below lists the numbers for the last 11 games
  that he played.
• a) From the data, can the player predict the
  points that he will score if he knows how much
  ice-time that he will get?
• b) According to the regression line, how much
  ice-time must he get to score at least 1 point?
• c) Is it realistic to use this linear model to
  make this prediction?

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12. The table and the graph below presents 9
car speed records established over 109 years of
the history of the car.
a) Establish and qualify the statistic relation
between the speed record and the year.
b) From the regression line, determine the speed
record established in 1974.