A sample of 25 randomly selected students has a mean test score of 81.5 with a standard deviation of 10.2. Assuming that the population has a normal distribution, use this sample data to construct a 95% confidence interval for the population mean μ of all test scores.
A. (77.29, 85.71)
B. (56.12, 78.34)
C. (87.12, 98.32)
D. (66.35, 69.89)
Answer:
Given,
n = 25
Mean = 81.5
Standard deviation = 10.2
To give the 95% confidence interval
Degree of freedom = n - 1
= 25 - 1
= 24
Alpha = 0.05
alpha/2 = 0.025
Here for 95% confidence interval , corresponding alpha 0.025 & degree of freedom 24 the critical value t 0.025,24 is 2.064
So consider,
Interval = Xbar +/- t*s/sqrt(n)
substitute the values
= 81.5 +/- 2.064*10.2/sqrt(25)
= 81.5 +/- 4.21
= (81.5 - 4.21 , 81.5 + 4.21)
= (77.29 , 85.71)
Interval = (77.29 , 85.71)
So Option A is right answer.
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