Question

Given: Assume you have collected data from 150 subjects, and that the distribution of the data is a "normal" distribution. The mean of the scores is 37, with a standard deviation of 4.5. Using the given information, calculate the 68% confidence interval. A confidence interval represents a range of values, the lowest value is references as the "lower bound", the highest value is referenced as the "upper bound". Determine the lower and upper bounds for the 68% confidence interval. Round your answer for each value to a single decimal place (e.g. 36.63 rounds to 36.6).

Lower Bound =

Upper Bound =

Answer 1

Solution :

Given that,

= 37

= 4.5

n = 150

At 68% confidence level the z is ,

  = 1 - 68% = 1 - 0.68 = 0.32

/ 2 = 0.32 / 2 = 0.16

Z_/2 = Z_0.16 = 0.995

Margin of error = E = Z_/2* ( /n)

= 0.995 * (4.5 / 150)

= 0.37

At 68% confidence interval estimate of the population mean is,

- E < < + E

37 - 0.37< < 37 + 0.37

36.63< < 37.37

(36.63 ,  37.37 )

lower bound =36.63

upper bound = 37.37