Question

The mean age for all Foothill College students for a recent Fall term was 33.2. The population standard deviation has been pretty consistent at 15. Suppose that twenty-five Winter students were randomly selected. The mean age for the sample was 30.4. We are interested in the true mean age for Winter Foothill College students. Let X = the age of a Winter Foothill College student.

Construct a 95% Confidence Interval for the true mean age of Winter Foothill College students by working out then answering the exercise.

Identify the following specifications. (Round your answers to two decimal places.)
(a) lower limit


(b) upper limit


(c) error bound

Answer 1

Answer:

a) Lower Limit = 24.52

b) Upper Limit = 36.28

c) Error bound = 5.88

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 33.2

Sample mean, $\bar{x}$ = 30.4

Sample size, n = 25

Alpha, α = 0.05

Population standard deviation, σ = 15

95% Confidence interval:

$\mu \pm z_{critical}\frac{\sigma}{\sqrt{n}}$

Putting the values, we get,

$z_{critical}\text{ at}~\alpha_{0.05} = \pm 1.96$

$30.4 \pm 1.96(\frac{15}{\sqrt{25}} ) = 30.4 \pm 5.88 = (24.52,36.28)$

a) Lower Limit = 24.52

b) Upper Limit = 36.28

c) Error bound

$\text{Margin of error} = z_{critical}\times \displaystyle\frac{\sigma}{\sqrt{n}}\\\\= 1.96\times \frac{15}{\sqrt{25}} = 5.88$