Use the normal distribution to find a confidence interval for a proportion p given the relevant sample results. Give the best point estimate for p, the margin of error, and the confidence interval. Assume the results come from a random sample. A 99% confidence interval for p given that p-hat = 0.34 and n= 500. Point estimate ___ (2 decimal places) Margin of error (3 decimal places) The 99% confidence interval is to _ (3 decimal places)

Answers

Answer 1

Answer:

Answer:

(a) The point estimate for the population proportion p is 0.34.

(b) The margin of error for the 99% confidence interval of population proportion p is 0.055.

Step-by-step explanation:

A point estimate of a parameter (population) is a distinct value used for the estimation the parameter (population). For instance, the sample mean $\bar x$ is a point estimate of the population mean μ.

Similarly, the the point estimate of the population proportion of a characteristic, p is the sample proportion $\hat p$ .

The (1 - α)% confidence interval for the population proportion p is:

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

The margin of error for this interval is:

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

The information provided is:

$\hat p=0.34\nn=500\n(1-\alpha)\%=99\%$

(a)

Compute the point estimate for the population proportion p as follows:

Point estimate of p = $\hat p$ = 0.34

Thus, the point estimate for the population proportion p is 0.34.

(b)

The critical value of z for 99% confidence level is:

$z={\alpha/2}=z_(0.01/2)=z_(0.005)=2.58$

*Use a z-table for the value.

Compute the margin of error for the 99% confidence interval of population proportion p as follows:

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

$=2.58\sqrt{(0.34(1-0.34))/(500)}$

$=2.58* 0.0212\n=0.055$

Thus, the margin of error for the 99% confidence interval of population proportion p is 0.055.

(c)

Compute the 99% confidence interval of population proportion p as follows:

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

$CI=\hat p\pm MOE$

$=0.34\pm 0.055\n=(0.285, 0.395)$

Thus, the 99% confidence interval of population proportion p is (0.285, 0.395).

Answer 2

Answer:

Final answer:

The point estimate for p is 0.34. The margin of error, calculated using a z-score of 2.576, is 0.034. The 99% confidence interval is from 0.306 to 0.374.

Explanation:

This question is about calculating a confidence interval for a proportion using the normal distribution. The best point estimate for p is the sample proportion, p-hat, which is 0.34.

For a 99% confidence interval, we use a z-score of 2.576, which corresponds to the 99% confidence level in a standard normal distribution. The formula for the margin of error (E) is: E = Z * sqrt[(p-hat(1 - p-hat))/n]. Substituting into the formula, E = 2.576 * sqrt[(0.34(1 - 0.34))/500] = 0.034.

The 99% confidence interval for p is calculated by subtracting and adding the margin of error from the point estimate: (p-hat - E, p-hat + E). The 99% confidence interval is (0.34 - 0.034, 0.34 + 0.034) = (0.306, 0.374).

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The perimeter of a rectangle is 52 feet. Describe the possible lengths of a side if the area of the rectangle is not to exceed 120 square feet. I need to find the solution set for this.

Answers

Answer:

2x+2y=52

x*y=120

Step-by-step explanation:

Final answer:

The possible lengths of a side of the rectangle are 22, 21, 20, 19, 18, 17, 16 feet.

Explanation:

To find the possible lengths of a side of the rectangle, let's use the formula for the perimeter of a rectangle, which is 2(length + width). We can set up an equation using the given information:

2(length + width) = 52

Dividing both sides by 2, we get:

length + width = 26

Now, to find the possible lengths, we need to consider the area. The formula for the area of a rectangle is length x width. We are given that the area is not to exceed 120 square feet, so we can set up the inequality:

length x width <= 120

Using the relationship length + width = 26, we can substitute length = 26 - width into the inequality:

(26 - width) x width <= 120

Simplifying the inequality, we get:

-width^2 + 26width - 120 <= 0

Now, we can solve this quadratic inequality to find the range of possible widths. Once we have the widths, we can substitute them back into the equation length + width = 26 to find the corresponding lengths.

By solving the quadratic inequality, we find that the possible widths are 4 <= width <= 10. Substituting these widths back into the equation length + width = 26, we get the corresponding lengths:

If width = 4, then length = 22

If width = 5, then length = 21

If width = 6, then length = 20

If width = 7, then length = 19

If width = 8, then length = 18

If width = 9, then length = 17

If width = 10, then length = 16

The possible lengths of a side of the rectangle are {22, 21, 20, 19, 18, 17, 16} feet.

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Write 5⁴ in expanded form. Then share the value of this exponent.

Answers

Answer: 626

Step-by-step explanation:

5x5x5x5 = 625

Square root of 29 and need to show work please

Answers

Answer:

5.38

Step-by-step explanation:

$√(29)$

Please help me with this

Answers

Answer:

28.24

Step-by-step explanation:

25 + 32/10 + 4/100

take lcm of the denominator

lcm = 100

25*100 + 32*10 +4*1/100

2500 + 320 +4/100

2824/100

28.24

Find the value of (1 point)

Answer D .28.24

Tanya enters a raffle at the local fair, and is wondering what her chances of winning are. If her probability of winning can be modeled by a beta distribution with α = 5 and β = 2, what is the probability that she has at most a 10% chance of winning?

Answers

Answer:

$P(X<0.1)= 5.5x10^(-5)$

Step-by-step explanation:

Previous concepts

Beta distribution is defined as "a continuous density function defined on the interval [0, 1] and present two parameters positive, denoted by α and β, both parameters control the shape. "

The probability function for the beta distribution is given by:

$P(X)= (x^(\alpha-1) (1-x)^(\beta -1))/(B(\alpha,\beta))$