Question

Below are means, standard deviations, and sample sizes of three different data sets. Estimate the 90% confidence interval for dataset A, 95% for data set B, and 99% for set C.

Set A: mean=6300, standard deviation= 300, n=200

Set B: mean=65, standard deviation= 15, n=75

Set C: mean=93, standard deviation= 37, n=200

Answer 1

a) x_bar =6300

   = 300

n=200

So 90% confidence interval is given by

CI = x_bar   z*/sqrt (n)

= 6300 1.64 * 300/sqrt(200)

= 6300 34.7897

CI = 6300 - 34.7897 and CI = 6300 + 34.7897

CI = 6265.21 CI = 6334.79

So 90 % confidence interval is (6265.21,6334.79)

b) x_bar = 65

= 15

n=75

So 95% confidence interval is given by

CI = x_bar   z* (/sqrt (n))

= 65 1.96* 15/sqrt(74)

= 65 3.39

CI = 65 - 3.39 and CI = 65 + 3.39

= 61.61 CI = 68.39

So 95 %confidence interval is (61.61,68.39)

c) given

X_bar = 93

= 37

n=200

So 99% confidence interval is given by

CI = x_bar z* /sqrt (n)

= 93 2.58 * 37/sqrt (200)

= 93 6.75

CI = 93 - 6.75 and CI = 93 + 6.75

= 86.25 CI = 99.75

So 99% confidence interval is (86.25,99.75)