14 children sample size were learning to ride twowheel bikes

14 children (sample size), were learning to ride two-wheel bikes. It was revealed that it takes them an average of 6 months (sample average) with a sample standard deviation of 3 months.

Construct a 90% confidence interval for the population mean length of time needed to learn how to ride two-wheel bikes.

(Population standard deviation is not known. For Margin of Error use t-value from attached Appendix Table for t-Distribution)

Solution

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 =    0.05          
X = sample mean =    6          
t(alpha/2) = critical t for the confidence interval =    1.770933396          
s = sample standard deviation =    3          
n = sample size =    14          
df = n - 1 =    13          
Thus,              
              
Lower bound =    4.580094424          
Upper bound =    7.419905576          
              
Thus, the confidence interval is              
              
(   4.580094424   ,   7.419905576   ) [ANSWER]