The SmartMinds University collects a variety of statistics about its students.Â The database includes the following data:
(a)Â Studentâ€™s academic class {Freshman, Sophomore, Junior, Senior}Â
(b)Â Studentâ€™s ethnicity
(c)Â Studentâ€™s age category: {1820, 2125, 2630, over 30}Â
(d)Â Studentâ€™s preferred classroom temperature (in degrees Fahrenheit)Â
(e)Â Studentâ€™s height and weight
(f)Â Number of students in each dorm room
(g)Â Studentâ€™s year of birth
(h)Â Studentâ€™s satisfaction rating on a scale of 110
(i)Â If the student smokes {yes, no}Â
(j)Â Â Â Studentâ€™s preferred TV channel {Entertainment, History, HBO, CNN, ESPN}
Â
[A (10 points)]
For each of the questions, indicate with an â€œXâ€ what scale the data is measured on.
QuestionÂ NominalÂ OrdinalÂ IntervalÂ Ratio
(a)Â Â Â Â
(b)Â Â Â Â
(c)Â Â Â Â
(d)Â Â Â Â
(e)Â Â Â Â
(f)Â Â Â Â
(g)Â Â Â Â
(h)Â Â Â Â
(i)Â Â Â Â
(j)Â Â Â Â
[B (10 points)]
For each of the questions, indicate with an â€œXâ€ if the measurement is Qualitative, Quantitative Discrete or Quantitative Continuous.
QuestionÂ QualitativeÂ Quantitative DiscreteÂ Quantitative Continuous
(a)Â Â Â
(b)Â Â Â
(c)Â Â Â
(d)Â Â Â
(e)Â Â Â
(f)Â Â Â
(g)Â Â Â
(h)Â Â Â
(i)Â Â Â
(j)Â Â Â
Â
[C (12 points)]
GRE Scores: The following are the quantitative GRE scores of the graduate students from one of the Mathematics department:Â
777Â 765Â 758Â 788Â 766Â 750Â 759Â 755Â 788Â
749Â 758Â 742Â 780Â 740Â 765Â 787Â 766Â 766Â
a. Construct a grouped frequency distribution with 5 classes.
b. Use Excel to construct a Histogram.Â (Tools ïƒ Data Analysis ïƒ Histogram ïƒ for input range select the given values, for the bin range select the classes upper boundaries values ïƒ check Chart Output)
Note: give a brief explanation by specifying the covered steps.
Highest
Lowest
Range
Class width
Grouped frequency distribution
Class limitsÂ Class boundariesÂ Frequency
Â Â
Â Â
Â Â
Â Â
Â Â
Â [D (13 POINTS)]
For the set of data given above (on point C), calculate the following descriptive statistics (Briefly explain the median, mode, and quartiles. For quartiles calculations, follow the way is explained in the homework2).Â You can use any excel tools as long as you show your work.
MeanÂ
MedianÂ
ModeÂ
1ST QuartileÂ
3rd QuartileÂ
Interquartile RangeÂ
RangeÂ
Standard DeviationÂ
VarianceÂ
b.Â Â Compute the zscores.Â Give the formula you used.
[E (10 points)]
SmartMinds University is running a promotional raffle that offers a chance to win either a 1year discount on tuition cost (which results in a $500 savings) or a 2year discount on bookstore purchases (which results in a $300 savings).Â
â€¢Â Winning a tuition discount has a 1in500 chance.
â€¢Â Winning a bookstore purchases discount has a 1in20 chance.
Is this promotion worth it if the tickets cost $20?Â
Â
B.Â Determine the appropriate statistical term:
Selecting 64 customers to study without regard to their data is called creating a(n) _________.Â
The data for all customers is called a(n) _______.Â
Â [F1 (15 points)]Â ONLY if you cannot answer F1, for partial credit (8 points) answer F2.
Some additional collected data is presented in the table below:
Â
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Age Category
CollegeÂ {1820}Â {21 â€“ 25}Â {2630}Â Above 30Â
KingsÂ 500Â 100Â 400Â 100Â
FalconÂ 300Â 250Â 100Â 200Â
PriestleyÂ 900Â 700Â 800Â 600Â
Â Â Â Â Â
Give the literal formula first (not with numbers) and then solve:
â€œWhat is the probability of being in the lowest age category given that you are a student of Priestley College?â€Â
Give the literalÂ formula first (not with numbers) and then solve:
â€œWhat is the probability of being either a Kings College or a Falcon College student?â€Â
Give the literal formula first (not with numbers) and then solve: â€œWhat is the probability of being younger than 26 years given that you are a student of Priestley College?â€ Â
Give the literalÂ formula first (not with numbers) and then solve:
â€œWhat is the probability of not being a student of Kings College?â€Â
Is there any relationship between being a member older than 30 and belonging to a specific College? (relationship between age and College)Â
[F2 (8 points)]
Another survey examined the studentâ€™s preferences in having lunch available on campus.
Â Have Lunch (L)Â Not have Lunch (Lâ€™)Â
Male Student (M)Â 2500Â 3000Â
Female Student (F)Â 1700Â 1000Â
Â Â Â
a) Compute the Marginal Probabilities and the Joint Probabilities.
Marginal ProbabilityÂ Joint Probability
Â
Â
Â
Â
b) Compute: P(LM), P(M or L)Â Â
[G (30 points)]
Overall, the studentsâ€™ class attendance days (per year academic) is normally distributed around 180 days with a standard deviation of 20 days.
Whatâ€™s the probability that the mean number of attendance days will be between 190 and 200?Â
Students that are in the top 10% will receive a 20% off coupon at the â€œCrazyâ€ cafeteria.Â What is the minimum number of attendance days that you should have in order to receive such discount? Â
The students at or below the 15%ile of number of attendance days must attend a counseling session with one of the advisers. At least how many attendance days you should have in order to not have to attend such session?Â
How likely (what is the probability) is it that Cri (name not previously mentioned) will have her attendance days between 170 and 195 days?Â
What percentile does an attendance of 200 attendance days rank at?
What percentile does an attendance of 180 attendance days rank at?Â
How likely (what is the probability) is it to have the number of days attended below 170? Â
If 36 students (36 = size of the sample) selected randomly attended the school, whatâ€™s the likelihood that their mean number of attended days will be within 2 days of the population mean? (mean +/ 2)
Â
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