Given:△SAL, SA = LA AT −

At a large Midwestern university, a simple random sample of 100 entering freshmen in 1993 found that 20 of the sampled freshmen

guajiro [1.7K]

Answer:

The 90% confidence interval for the difference of proportions is (0.01775,0.18225).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

p1 -> 1993

20 out of 100, so:

$p_1 = \frac{20}{100} = 0.2$

$s_1 = \sqrt{\frac{0.2*0.8}{100}} = 0.04$

p2 -> 1997

10 out of 100, so:

$p_2 = \frac{10}{100} = 0.1$

$s_2 = \sqrt{\frac{0.1*0.9}{100}} = 0.03$

Distribution of p1 – p2:

$p = p_1 - p_2 = 0.2 - 0.1 = 0.1$

$s = \sqrt{s_1^2+s_2^2} = \sqrt{0.04^2 + 0.03^2} = 0.05$

Confidence interval:

$p \pm zs$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

90% confidence level

So $\alpha = 0.1$ , z is the value of Z that has a p-value of $1 - \frac{0.1}{2} = 0.95$ , so $Z = 1.645$ .

The lower bound of the interval is:

$p - zs = 0.1 - 1.645*0.05 = 0.01775
$

The upper bound of the interval is:

$p + zs = 0.1 + 1.645*0.05 = 0.18225
$

The 90% confidence interval for the difference of proportions is (0.01775,0.18225).

6 0

3 years ago

A bag contains 3 yellow, 1 red, 2 green beads. Charlene draws a bead, keeps it out, then draws another bead. What’s the probabil

CaHeK987 [17]

Charlene had more green then red.

so She will run out of red first anyways because its the lowest amount.

Hope this helps....

5 0

3 years ago

A stained glass window is going to be installed in a semi-circular opening, which is above a 30 inch wide door. If the stained g

xenn [34]

The answer is $494.55

Let's first imagine a circle and calculate its area and then reduce it in half for the area of a semi-circle. Since this opening is above a 30-inch wide door, the circle will have a diameter of 30 inches.
The area of the circle (A) is:
A = π · r²
where:
π = 3.14
r - radius: r = diameter ÷ 2 = 30 ÷ 2 = 15 inches

So, the area of the circle is:
A = π · r² = 3.14 · 15² = 706.5 inches²

The area of the semicircle is half of the area of the circle:
A1 = A ÷ 2 = 706.5 ÷ 2 = 353.25 inches²

Since the stained glass window costs $1.40 per square inch, for 353.25 square inches it will cost $494.55:
353.25 square inches * 1.40 $/square inch = $494.55

4 0

3 years ago

Josh walks 18 dogs each week. Today, he is walking 1/3 of the dogs. How many dogs is he walking today?

Amiraneli [1.4K]

18*(1/3) (or one third of eighteen) = 6 dogs

4 0

4 years ago

Plz can u answer the questions I have attached

vodomira [7]

Answer:

For the first question it is 2.

2 x 2 = 4

5 x 2 = 10

4 + 10 - 14 = 0

The second question is -2

-2 x -2 = 4

5 x -2 = -10

4 + -10 + 6 = 0

Hope this helps

Step-by-step explanation:

4 0

3 years ago