Use the following sample to estimate a population mean .

Question

Use the following sample to estimate a population mean �.

30.8	59.7	41.5	62.6
29.5	57	35.4	37.7
48.1	45	58	28
57.5	54.7	57.3

Find the 90% confidence interval about the population mean. Enter your answer as a tri-linear inequality accurate to two decimal place.

Answer 1

Hi Emma,

We were not given a population standard deviation, so we use a t-confidence interval:

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

Now, use a TI-80s series calculator or statistical software to get the sample mean (xbar) and standard deviation (s).

xbar = 46.85

s = 12.21

Now, we need the degrees of freedom, which is:

df = n-1

df = 15 -1 = 14

From t-table t*(90%, 14) = 1.761

We still need standard error:

SE= s/sqrt(n)

SE = 12.21/sqrt(15)

SE = 3.15

CI= 46.85 +/- (1.761*3.15)

CI= (41.30, 52.40)

I hope this helps. I noticed you have a couple confidence interval problems up here. We can schedule a tutoring session via Wyzant to talk through these.