Caitlin says that AC is the longest segment of fencing

A sample of 900 college freshmen were randomly selected for a national survey. Among the survey participants, 372 students were

Rufina [12.5K]

Answer:

a) $ME=2.58 \sqrt{\frac{0.413(1-0.413)}{900}}=0.0423$

b) $0.413 - 2.58 \sqrt{\frac{0.413(1-0.413)}{900}}=0.371$

Step-by-step explanation:

1) Data given and notation

n=900 represent the random sample taken

X=372 represent the students were pursuing liberal arts degrees

$\hat p=\frac{372}{900}=0.413$ estimated proportion of students were pursuing liberal arts degrees

$\alpha=0.01$ represent the significance level

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

p= population proportion of students were pursuing liberal arts degrees

2) Solution to the problem

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=2.58$

The margin of error is given by:

$ME=z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

If we replace we have:

$ME=2.58 \sqrt{\frac{0.413(1-0.413)}{900}}=0.0423$

And replacing into the confidence interval formula we got:

$0.413 - 2.58 \sqrt{\frac{0.413(1-0.413)}{900}}=0.371$

$0.413 + 2.58 \sqrt{\frac{0.413(1-0.413)}{900}}=0.455$

And the 99% confidence interval would be given (0.371;0.455).

We are confident (99%) that about 37.1% to 45.5% of students were pursuing liberal arts degrees.

7 0

3 years ago

Graph y=0.4x............................

Leto [7]

Answer:

Look at the image below

8 0

4 years ago

Read 2 more answers

-13 +n + 5 + 6 = 5 + 4n-4

natta225 [31]

Answer:

n=-1

Step-by-step explanation:

-13+n+5+6=5+4n-4

n-2=4n+1

-2=3n+1

-3=3n

-1=n

4 0

3 years ago

What is 12z+42=73 solve for x

Sholpan [36]

12z+42=73
subtract 42 from both sides.
12z=31
divide 12 on both sides to get:
z=2.58

6 0

3 years ago

Justin jogged for four days in a row. He jogged 2 miles the first day. On the second day, he jogged 75% of the distance he jogge

Anarel [89]

Answer:

2.75 miles jogged on the fourth day

Step-by-step explanation:

Justin jogged 2 miles on the first day.

On the second day he jogged 75% of 2 miles. To find 75% of 2 miles we need to divide by 100 and multiply by 75.

2 / 100 = 0.02 x 75 = 1.5 miles jogged on the second day. (3.5 miles jogged in total so far)

On the third day he jogged 1.5 miles more than the last day:

1.5 + 1.5 = 3 (6.5 miles jogged so far)

9.25 total miles were jogged, meaning that we will need to subtract 6.5 from 9.25 to get the answer:

9.25 - 6.5 = 2.75 miles jogged on the fourth day

3 0

3 years ago