If a random sample of 53 students was asked for the number of semester hours they are taking this semester. The sample standard deviation was found to be s = 4.7 semester hours.…

Question

asked Jan 12, 2021 203k views

1 Answer

Vinnydiehl · Answer 1 · 2021-01-17T08:31:17+0000

Answer:

94 more students should be included in the sample.

Explanation:

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

$\alpha = (1-0.99)/(2) = 0.005$

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

So it is z with a pvalue of
1-0.005 = 0.995 , so
z = 2.575

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.

How many students we need to sample to be 99% sure that the sample mean x is within 1 semester hour of the population mean?

We need to survey n students.

n is found when M = 1.

We have that
$\sigma = 4.7$

So

$M = z*(\sigma)/(√(n))$

1 = 2.575*(4.7)/(√(n))

√(n) = 2.575*4.7

(√(n))^(2) = (2.575*4.7)^(2)

n = 146.47

Rounding up

147 students need to be surveyed.

How many more students should be included...?

53 have already been surveyed

147 - 53 = 94

94 more students should be included in the sample.