A new sports equipment company, Sports EQUIP, sold 2,835 helmets in their second year

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

2nd term of (2r-3s)^12

earnstyle [38]

Answer:

1.-12*(2r)^11 * (3s)

= -12*2048*3 r^11 s

= -73728 r^11 s

2.12C1 (2r)¹¹(-3s) = -36(2¹¹)r¹¹s = -73728r¹¹s

3.24 r - 36 s

The second term: -36 s

4.(2r-3s)^12

= (2r)^12 + 12C1 (2r)^11 (-3s)

= 2^12 r^12 + (12) 2^11 r^11 (-3) s

= 4096 r^12 - (12)(3)(2098) r^11 s

= 4096 r^12 - 73,728 r^11 s + .....

-73,728 r^11 s

Step-by-step explanation:

Yan lang po alam ko at nahirapan ako e solved yan hehe pero hope it helps

4 0

3 years ago

What is the initial population of Rock Springs ?

Ostrovityanka [42]

C) 46,200
This is because the 1,900 represents the increase in population in x years.

5 0

3 years ago

If the dimensions of a pentagonal prism are quadrupled, then the surface area of the prism is multiplied by eight.

Lubov Fominskaja [6]

Answer:

false

Step-by-step explanation:

the relationship between lengths/dimensions and areas is that areas are created by multiplying 2 dimensions.

when you quadruple (×4) the dimensions, then the areas are growing with the square of the factor (×4×4 = ×16), because the factor goes twice into the multiplication : one time for every dimension involved.

so, quadrupling the dimensions would multiply the areas by 16.

8 0

3 years ago

Which of the following is not an integer?

In-s [12.5K]

Answer:

$-\frac{54}{7}$