MAT107 Name: Statistics Final Exam Prof: FELKER 1. Conceptual Questions a) Give three examples of a continuous random variable. b) Give two examples of a voluntary response sample. Why is a voluntary...

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Answer To: MAT107 Name: Statistics Final Exam Prof: FELKER 1. Conceptual Questions a) Give three examples of a...

Saravana answered on May 18 2021
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MAT107                                        Name:
Statistics                Final Exam
Prof: FELKER
1. Conceptual Questions
a) Give three examples of a continuous random variable.
· Age of the participants in a survey
· Weight of the participants in a survey
· Number of hours per day of TV watching self reported by participants in a survey.
b)
Give two examples of a voluntary response sample. Why is a voluntary response sample considered to be a poor sampling technique?
A voluntary response sample contains volunteers to be included in the survey or study.
Disadvantages:
· The survey over represents people with strong opinion and under represents people with no opinion about the issue.
· The researcher has no control over the demographic composition of the participants.
Example:
1. TV program viewer polls:
Only people who want to call in and be part of sample will bother to do it.
2. A website surveys readers asking for opinion on gun permits
The above two are voluntary as respondents volunteer to participate. The responses to the survey will be skewed towards people who have strong opinion about the subject of the survey.
2. Football Player Weights – Listed below are the weights in pounds of 11 players randomly selected from the roster of the Seattle Seahawks when they won Super Bowl XLVIII. Are the results likely to be representative of all National Football League players? Why or why not?
189, 254, 235, 225, 190, 305, 195, 202, 190, 252, 305
For the above data find (a) the mean, (b) the median, (c) the mode, and (d) the midrange.
The sample of only 11 players weights is not representative of all NFL players.
Mean = (189+254+235+225+190+305+195+202+190+252+305)/ 11
Mean = 2542 / 11 = 231.09 pounds
Median:
Step1: Arranging the data in increasing order
189 190 190 195 202 225 235 252 254 305 305
Step2:
Median = ((n +1)/2) sample
Median = (12/2) = 6th sample = 225 pounds
Mode: There are two modes
190 and 305 pounds appear twice so there are two modes in the sample: 190 and 305 pounds
Midrange = (maximum value – minimum value)/2
From the ordered sample:
Midrange = (305-189)/2
Midrange = 116 / 2 = 58
3. For the grouped frequency distribution below find the (a) mean and (b) modal class.
Ages (in years) of Best Actor when an Oscar was won. – 87 male actors, who won an Oscar, were selected and this grouped frequency table was obtained reflecting the age at which the Oscar was won for the particular sample.
(Note – Extra columns in the table for your use.)
    Age (years) when Oscar was won
    Frequency
    Midpoint of age
    Frequency
    Midpoint X frequency
    20 -29
    1
    24.5
    1
    24.5
    30-39
    28
    34.5
    28
    966
    40-49
    36
    44.5
    36
    1602
    50-59
    15
    54.5
    15
    817.5
    60-69
    6
    64.5
    6
    387
    70-79
    1
    74.5
    1
    74.5
            
Sum = 3871.5; :
Mean = sum / n = 3871.5 / 87 = 44.5
Modal class: Age group 40-49 has most number of Oscar winners so the modal class interval is 40-49 years.
4. Find the range, variance, and standard deviation.
Assume the data represent samples, and use the shortcut formula for the unbiased estimator to compute the variance and standard deviation....
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