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Bookmarks People Window Help plus.com/edugen/student/mainfruni Practice Assignment Gradebook ORION please Answer This proble x ignment FULL SCREEN PRINTER VI Question 25 suppose the following data are selected randomly from a population of normally distributed values. 40 51 43 48 42 57 54 39 40 48 45 39 47 Construct a 95% confidence interval to estimate the population mean. (Round the intermediate values to 2 decimal places, Round your answers to 2 decimal places.) s US Question Attempts: o of 2 used SAVE FOR Copyright o 2000-2016 by John Wiley & Sons, Inc. or related companies Ail rights reserved. oceglicy I g2000-2016 lohn wilay sons. Ins All Rights Reserved. A Division of lohn.Wileuasonsauos. horedlassignment/test/aglist.unia

Explanation / Answer

25.

Note that              
              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    45.61538462          
t(alpha/2) = critical t for the confidence interval =    2.18          
s = sample standard deviation =    5.867118281          
n = sample size =    13          
df = n - 1 =    12          
Thus,              
              
Lower bound =    42.0679887          
Upper bound =    49.16278053          
              
Thus, the confidence interval is              
              
(   42.0679887   ,   49.16278053   ) [ANSWER]

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Hi! If you use z distirbution [even though sigma is unknown], please use this alternative:

Note that              
              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    45.61538462          
z(alpha/2) = critical z for the confidence interval =    1.96          
s = sample standard deviation =    5.867118281          
n = sample size =    13          
              
Thus,              
              
Lower bound =    42.42598279          
Upper bound =    48.80478644          
              
Thus, the confidence interval is              
              
(   42.42598279   ,   48.80478644   ) [ALTERNATIVE ANSWER]

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