Question
In: Statistics and Probability
1. A sample of 49 units drawn from a normally distributed population results in a sample...
1. A sample of 49 units drawn from a normally distributed population results in a sample mean of 18 and sample variance of 4. Use the t-distribution to find the 90% confidence interval for the mean. What is the lower limit?
2. A sample of 49 units drawn from a normally distributed population results in a sample mean of 18 and sample variance of 4. Use the t-distribution to find the 95% confidence interval for the mean. What is the lower limit?
Solutions
Expert Solution
Formula for Confidence Interval for Population mean when population Standard deviation is not known
1.
for 90% confidence level = (100-90)/100=0.10
/2
= 0.10/2=0.05
Sample size: n= 49
:
Sample mean : 18
s: Sample standard deviation = 
90% confidence interval for the mean
90% confidence interval for the mean : (17.5208,18.4792)
Lower limit = 17.5208
2.
95% confidence interval for the mean
for 95% confidence level = (100-95)/100=0.05
/2
= 0.05/2=0.025
Sample size: n= 49
:
Sample mean : 18
s: Sample standard deviation =
95% confidence interval for the mean
95% confidence interval for the mean : (17.4255,18.5745)
Lower limit = 17.4255
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