A pair of shoes is on sale for $51, which is a 25%

In a study of government financial aid for college students, it becomes necessary to estimate the percentage of full-time coll

algol13

Answer:

(a) The sample size required is 2401.

(b) The sample size required is 2377.

(c) Yes, on increasing the proportion value the sample size decreased.

Step-by-step explanation:

The confidence interval for population proportion p is:

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

The margin of error in this interval is:

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

The information provided is:

MOE = 0.02

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

(a)

Assume that the proportion value is 0.50.

Compute the value of n as follows:

$MOE=z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\0.02=1.96\times \sqrt{\frac{0.50(1-0.50)}{n}}\\n=\frac{1.96^{2}\times0.50(1-0.50)}{0.02^{2}}\\=2401$

Thus, the sample size required is 2401.

(b)

Given that the proportion value is 0.55.

Compute the value of n as follows:

$MOE=z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\0.02=1.96\times \sqrt{\frac{0.55(1-0.55)}{n}}\\n=\frac{1.96^{2}\times0.55(1-0.55)}{0.02^{2}}\\=2376.99\\\approx2377$

Thus, the sample size required is 2377.

(c)

On increasing the proportion value the sample size decreased.

8 0

4 years ago

Jessica has $35.She gives 2/5 oh her money to her sister.How much money did she give her sister?

omeli [17]

She gave $14 to her sister.

Explanation:
The word "of" in fraction word problems USUALLY signals for you to multiply. So, we want to find 2/5 of 35, so we multiply 2/5 x 35. That gives us 14, therefore she gave $14 to her sister

6 0

3 years ago

A cube-shaped hole is cut in a rectangular prism as shown below.

IgorC [24]

Surface area of the prism is 2xy+2xz+2yz
I think, we can cut hole on the face of the prisma 40x30, and size of the whole will be 5X5X5
hole increases surface area. If side of the cube is "a", then a^2 is the area of the one face of the cube.
when we are doing the hole, we remove 2 faces and add 4 more faces, so
2xy+2xz+2yz-2a^2+4a^2= 2xy+2xz+2yz+2a^2
So, 2*5*40+2*5*30+2*40*30+2*5^2=3150 cm^2
i hope it helps, it is what i can come up with now

6 0

4 years ago

Read 2 more answers

Which expression is equivalent to −1/4x+1/2?

Marat540 [252]

D. 1/4 (-x+2)

-x+2/4

3 0

3 years ago

Kylie invested $290 in an account paying an interest rate of 2.5% compounded

erik [133]

Answer:

11.9

Step-by-step explanation:

390=290e^(.025x)

x=11.85 which rounds to 11.9

7 0

3 years ago