A researcher might estimate the average height with the following sample heights

Question

A researcher must estimate the average height (in inches) with the following sample heights:

66.1

59

66.9

72.1

72.8

68.6

62.7

Assuming the population of heights are normally distributed, find the 90% confidence interval. Round the answers to two decimal places. Enter your answer as an interval of the form (LB,UP).

The researcher is 90% confident that the population average height is within the interval

Answer 1

Hi Emma,

You first need to compute the mean and standard deviation for your sample data. For mean, just add them up and divide by 7. For standard deviation, use a TI-80s series calculator or software. Manual computation is cumbersome as it involves repeated squared differences. From a TI-83:

xbar = 66.89

s = 4.92

Now, we only have sample standard deviation, not population, so we have to use a t-confidence interval. Formula is:

CI = xbar +/- t*SE, SE = standard error = s/sqrt(n)

xbar = sample mean

s= sample standard deviation

SE = standard error; s/sqrt(n)

n= sample size

Breaking down t*, you need degrees of freedom (df) along with your confidence level (90%). First:

df = n - 1 = 7 - 1 = 6

t_{6, 90} = 1.943

Therefore:

xbar = 66.89

t* = 1.943

s = 4.92

n = 7

SE = 4.92/sqrt(7) = 1.86

CI = 66.89 +/- (1.943 * 1.86)

CI = (63.28, 70.50)

I hope this helps.