Question

A random sample of 35 business students required an average of 50.7 minutes to complete a statistics exam. Assume that the population standard deviation to complete the exam was 10.4 minutes. The 95% confidence interval around this sample mean is ________. Group of answer choices (48.9, 52.5) (49.8, 51.6) (47.3, 54.1) (45.4, 56.0)

Answer 1

Answer:

(47.3, 54.1)

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$.

That is z with a pvalue of $1 - 0.025 = 0.975$, so Z = 1.96.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.96\frac{10.4}{\sqrt{35}} = 3.4$

The lower end of the interval is the sample mean subtracted by M. So it is 50.7 - 3.4 = 47.3

The upper end of the interval is the sample mean added to M. So it is 50.7 + 3.4 = 54.1

The answer is (47.3, 54.1).