A random sample of 13 students were asked how long it took them to complete a certain exam. The mean length of time was 117.6 minutes, with a standard deviation of 69.2 minutes. Find the lower bound of the 90% confidence interval for the true mean length of time it would take for all students to complete the exam. Round to one decimal place (for example: 108.1). Write only a number as your answer. Do not write any units.
Here n= 13 , = 117.6, s = 69.2
The confidence level = c = 0.90, so
Sample size is less than 30, so we find t interval. Hence df = n-1 = 13-1 = 12
The lower bound of 90% confidence interval is given by,
- E
Where,
tc = ----------( using excel formula " =t.inv.2t(0.10,12)" )
Hence,
= 34.20
Hence the lower bound is,
117.6 - 34.20 = 83.4
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