Question

In order for you to present numerical results in decimal form accurate to 0.01, it will be necessary for your intermediate calculations to be accurate to 0.001.

The mean age for King's College students for a recent Fall term was   31.4 . Suppose that   23   Winter students were randomly selected. The mean age for the sample was   33.8 . The sample standard deviation equals   11 . We are interested in the true mean age for Winter King's College students.

1.   x¯=   
2. 
   
3.   s=   
4. 
   
5. The standard error for   x¯=   
6. 
   
7. The   t   value for a   95%   confidence interval is   
8. 
   
9. Construct a   95%   confidence interval for the sample mean. Fill in the blanks to clarify the following diagram.
   

   LL   (lower limit)   =       UL   (upper limit)   =   
   
   

10. 
    
11. Is the mean age for the Fall term within our   95%   confidence interval for the mean age for the Winter term?    (pick one) YES/ NO

Answer 1

Ans

a) x- = 33.8 (sample mean age)

b) s = 11 (sample standard deviation)

c) Standard error = s/ (Sample size)0.5 = 11/230.5 = 2.2936

d) t value for level of significance 5% and degrees of freedom 22 = 2.07387

e) LL = x- - se*t = 33.8 - 2.07387*2.2936 = 29.0433

UL = x- + se*t = 33.8 + 2.07387*2.2936 = 38.556628

f) Yes, mean age of fell term is between the 95% confidence interval.

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