The director of student health at a large university is studying how many calori
ID: 2959805 • Letter: T
Question
The director of student health at a large university is studying how many calories students at her university consume in a day. She takes a random sample of 21 students from the population and records the number of calories they consume in a 24 hour period. From the sample, she found that the average number of calories consumed was 1879 and that standard deviation was 450. The director wishes to construct a 90% confidence interval for the mean number of calories consumed by the students.
What value of t is needed for this confidence level? 1
What is the margin of error for this confidence interval? 2
Using the statistics given above, calculate the confidence interval the director is looking for.
( ___3 ,____ 4 )
Explanation / Answer
Given n=21, xbar=1879, s=450
a=0.1
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What value of t is needed for this confidence level? 1
t(0.05, df=n-1=20)=1.72 (check student t table)
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What is the margin of error for this confidence interval? 2
margin of error = t*s/n = 1.72*450/sqrt(21) =168.9006
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Using the statistics given above, calculate the confidence interval the director is looking for.
xbar ± t*s/n
--> 1879 ± 168.9006
--> (1710.099, 2047.901)