Estimate the population mean

Question

Estimate the population mean by finding a 95% confidence interval given a sample of size 15, with a mean of 47.8 and a standard deviation of 11.2.

Correc

Confidence Interval: What is the 95% confidence interval to estimate the population mean? Enter your answer as an open-interval (i.e., parentheses) accurate to one decimal place.

Answer 1

Hi Emma,

We were given only a sample standard deviation, not a population standard deviation, so we have to use t. Formula for a t confidence interval is:

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

xbar = sample mean

t*= t-critical value obtained from t-table or software

s= sample standard deviation

n= sample size

Breaking down for this problem:

xbar = 47.8

To compute t*, we need the degrees of freedom. For a one-sample t-test, this is:

df = n -1

n = 15

df = 14

From t-table:

t*_{14, 95} = 2.145

So:

xbar = 47.8

t* = 2.145

s = 11.2

n= 15

SE = 11.2/sqrt(15)

SE = 2.89

CI = 47.8 +/- (2.145*2.89)

CI = (41.6, 54.0)

I hope this helps.