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

(47.3, 54.1)

Explanation:

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

`\alpha = (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(\sigma)/(√(n))`

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

`M = 1.96(10.4)/(√(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).