The formula used to compute a confidence interval for the me

The formula used to compute a confidence interval for the mean of a normal population when n is small is the following. x^^\\_ +/-\\(t text( critical value)\\)s/sqrt(n) What is the appropriate t critical value for each of the following confidence levels and sample sizes? (Round the answers to two decimal places.) (a) 95% confidence, n = 17 (b) 90% confidence, n = 12 (c) 99% confidence, n = 24 (d) 90% confidence, n = 24 (e) 80% confidence, n = 13 (f) 95% confidence, n = 10

Solution

The formula  used to compute a confidence interval for the mean of a normal population when n is small is the following.

xbar - tc * [ s/sqrt(n) ] and xbar + tc * [ s/sqrt(n) ]  

What is the appropriate t critical value for each of the following confidence levels and sample sizes?

EXCEL syntax : tinv(probability,d.f.)

where probability = alpha

d.f. = n - 1

a) for 95% confidence , n = 17

c = 0.95

alpha = 1-0.95 = 0.05

critical value = 2.12

b) 90% confidence, n = 12

c = 0.90

alpha = 1-0.90 = 0.1

critical value = 1.80

c)  99% confidence, n = 24

c = 0.99

alpha = 1-0.99 = 0.01

critical value = 2.81

d)  90% confidence, n = 24

c = 0.90

alpha = 1-0.90 = 0.1

critical value = 1.71

e) 80% confidence, n = 13

c = 0.80

alpha = 1-0.80 = 0.2

critical value = 1.36

f) 95% confidence, n = 10

c = 0.95

alpha = 1-0.95 = 0.05

critical value = 2.26