Homework SourseA student researcher is interested in determining the averag
A student researcher is interested in determining the average (µ) GPA of all FHSU students, in order to investigate grade inflation at regional universities. The data below represent the GPA\'s of thirty-six randomly selected FHSU students.
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| 2.75 | 2.55 | 3.95 | 1.74 | 2.66 | 3.10 | 2.41 | 1.57 | 2.12 | 3.67 | 3.56 | 1.98 | |||||||||||||||||||||||
| 4.00 | 3.21 | 1.95 | 3.75 | 1.45 | 3.01 | 2.29 | 2.66 | 3.95 | 2.50 | 3.88 | 2.79 | |||||||||||||||||||||||
| 2.32 | 3.44 | 2.07 | 0.62 | 2.72 | 3.55 | 3.92 | 3.41 | 2.14 | 1.15 | 2.75 | 3.25 |
A student researcher is interested in determining the average (µ) GPA of all FHSU students, in order to investigate grade inflation at regional universities. The data below represent the GPA\'s of thirty-six randomly selected FHSU students.
| ||||||||||||||||||||||||||||||||||
| 2.75 | 2.55 | 3.95 | 1.74 | 2.66 | 3.10 | 2.41 | 1.57 | 2.12 | 3.67 | 3.56 | 1.98 | |||||||||||||||||||||||
| 4.00 | 3.21 | 1.95 | 3.75 | 1.45 | 3.01 | 2.29 | 2.66 | 3.95 | 2.50 | 3.88 | 2.79 | |||||||||||||||||||||||
| 2.32 | 3.44 | 2.07 | 0.62 | 2.72 | 3.55 | 3.92 | 3.41 | 2.14 | 1.15 | 2.75 | 3.25 |
Solution
Alpha value is n\'t provided in the Question, Assuming alpha value = 0.90
d)
Margin of Error = t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
Mean(x)=2.7456
Standard deviation( sd )=0.8634
Sample Size(n)=36
Margin of Error = t a/2 * 0.8634/ Sqrt ( 36)
= 1.69 * (0.144)
= 0.243
e)
Confidence Interval
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=2.7456
Standard deviation( sd )=0.8634
Sample Size(n)=36
Confidence Interval = [ 2.7456 ± t a/2 ( 0.8634/ Sqrt ( 36) ) ]
= [ 2.7456 - 1.69 * (0.144) , 2.7456 + 1.69 * (0.144) ]
= [ 2.502,2.989 ]
f)
Interpretations:
1) We are 90% sure that the interval [ 2.502,2.989 ] contains the true population mean GPA\'s of all FHSU students
Alpha value is n\'t provided in the Question, Assuming alpha value = 0.95
d.
Margin of Error = t a/2 * 0.8634/ Sqrt ( 36)
= 2.03 * (0.144)
= 0.292
e.
Confidence Interval = [ 2.7456 ± t a/2 ( 0.8634/ Sqrt ( 36) ) ]
= [ 2.7456 - 2.03 * (0.144) , 2.7456 + 2.03 * (0.144) ]
= [ 2.453,3.038 ]
f.
Interpretations:
1) We are 90% sure that the interval [ 2.502,2.989 ] contains the true population mean GPA\'s of all FHSU students
