A student researcher is interested in determining the average (µ) GPA of all FHS
ID: 3389869 • Letter: A
Question
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. d. Determine the margin of error. e. Determine the confidence interval. f. In a sentence, interpret the contextual meaning of your result to part e above...that is relate the values to this situation regarding the mean GPA's of all 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 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. d. Determine the margin of error. e. Determine the confidence interval. f. In a sentence, interpret the contextual meaning of your result to part e above...that is relate the values to this situation regarding the mean GPA's of all 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 3.25Explanation / Answer
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
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