Select the correct answer.

A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than ex

Olenka [21]

Answer:

a

The 90% confidence interval that estimate the true proportion of students who receive financial aid is

$0.533 < p < 0.64$

b

$n = 1789$

Step-by-step explanation:

Considering question a

From the question we are told that

The sample size is n = 200

The number of student that receives financial aid is $k = 118$

Generally the sample proportion is

$\^ p = \frac{k}{n}$

=> $\^ p = \frac{118}{200}$

=> $\^ p = 0.59$

From the question we are told the confidence level is 90% , hence the level of significance is

$\alpha = (100 - 90 ) \%$

=> $\alpha = 0.10$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.645$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} }$

=> $E = 1.645 * \sqrt{\frac{0.59 (1- 0.59)}{200} }$

=> $E = 0.057$

Generally 90% confidence interval is mathematically represented as

$\^ p -E < p < \^ p +E$

=> $0.533 < p < 0.64$

Considering question b

From the question we are told that

The margin of error is E = 0.03

From the question we are told the confidence level is 99% , hence the level of significance is

$\alpha = (100 - 99 ) \%$

=> $\alpha = 0.01$

Generally from the normal distribution table the critical value of is

$Z_{\frac{\alpha }{2} } = 2.58$

Generally the sample size is mathematically represented as

$[\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p )$

=> $n = [\frac{2.58}{0.03} ]^2 * 0.59 (1 - 0.59 )$

=> $n = 1789$

8 0

3 years ago

Miriam is playing a simple game of dice. For every 1 or 6 rolled, Miriam will

Nat2105 [25]

Answer: Win $0.33

Step-by-step explanation:

5 0

2 years ago

(HELP PLEASE I BEG)The amount of money that Maria had in a savings account at the beginning of 2018 was $2,750. At the beginning

maks197457 [2]

Step-by-step explanation:

First, you need to find the difference 3201-2750=451, it has increased by 451, then divide the difference by the original number, which is 2750 because thats what she started off with (3201 would be the new number)

Increase% = Increase ÷ Original Number ×100

451÷2750×100=16.4%

7 0

3 years ago

Find the value of x.

Leokris [45]

Answer:

Therefore the value of $x=31\°$

Step-by-step explanation:

Given:

m∠ A = 56°

m∠ B = 75°

m∠ ACD = x°

To Find:

x = ?

Solution:

In Δ ABC

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

Here,

The opposite interior angles are angle A and angle B.

An exterior angle of a triangle is angle ACD which is x°

∴ $m\angle A +m\angle B=m\angle ACD\\$ ...Exterior angle property of Δ

Substituting the values we get

$56+75=x\\\\\therefore x=131\°$

Therefore the value of $x=31\°$

8 0

3 years ago

The air temperature at the beach is 97 degrees. The water temperature is 72 degrees. When you walk into the water, what is the p

Gnesinka [82]

The answer is simply all you do is subtract 72 from 97 and you'll have the answer which is 25, so the temperature decreased by 25 degrees

7 0

4 years ago