If the number of measurements is increased to 101 and the ne

If the number of measurements is increased to 101 and the new average (recalculated with all the new measurements) is 5’8.5” with a new standard deviation of 1.2”, with 90% confidence (all in inches and rounded to two decimal places):

a) What range of values do you expect the true mean to fall within? to

b) What range of values do you expect future measurements to fall within?

Solution

a)

n=101

SD =1.2 inches

Mean = 5\'8.5\" = 12*5 + 8.5 inches = 68.5 inches

z for 90% confidence interval = 1.645

Standard Error for True Mean = (z * SD)* sqrt(1/n)

= ( 1.645 * 1.2 ) * sqrt(1/101) = 0.2

Therefore, Confidence Interval ( or range of values) for true mean :

= (68.5 - 0.2 , 68.5 +0.2)

= (68.3 , 68.7) Answer

b)

n=101

SD =1.2 inches

Mean = 5\'8.5\" = 12*5 + 8.5 inches = 68.5 inches

z for 90% confidence interval = 1.645

Standard Error for Future Measurements = (z * SD)* sqrt(1+1/n)

= ( 1.645 * 1.2 ) * sqrt(1+1/101) = 1.98

Therefore, Confidence Interval ( or range of values) for Future Measurements :

= (68.5 -1.98 , 68.5 +1.98)

= (66.52 , 70.48) Answer