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You are interested in estimating the the mean age of the citizens living in your community. In order to do this, you plan on constructing a confidence interval; however, you are not sure how many citizens should be included in the sample. If you want your sample estimate to be within 5 years of the actual mean with a confidence level of 94%, how many citizens should be included in your sample? Assume that the standard deviation of the ages of all the citizens in this community is 22 years.

Answers

Answer 1

Answer:

The sample size is $n = 68$

Step-by-step explanation:

From the question we are told that

The margin of error is $E = 5 \ years$

The standard deviation is $\sigma = 22$

From the question we are told the confidence level is 94% , hence the level of significance is

$\alpha = (100 - 94 ) \%$

=> $\alpha = 0.06$

Generally from the normal distribution table the critical value of $(\alpha )/(2)$ is

$Z_{(\alpha )/(2) } = 1.881$

Generally the sample size is mathematically represented as

$n = [\frac{Z_{(\alpha )/(2) } * \sigma }{E} ] ^2$

=> $n = [\frac{1.881 } * 22 }{5} ] ^2$

=> $n = 68$

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a trapezoids longer base is 4 times its shorter base. If the trapezoid has an area of 80 cm squared and a height of 8cm has what is the length of each base

Answers

Long One is 16
Short One is 4!!

A=base+base/2 * height

A=80

16+4/2 = 10

10 * 8 = 80!!

Charlotte had $86. She spent $15 on a ticket to the zoo and then her mom gave her $24. How much money does Charlotte have now?

$____

Answers

she had 86 so she spent 15 and this mean subtracting 15,and her mom gave her 24 so we add 24
86-15+24=95$

She would have 95$
Have a great day hope it helps

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:

(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).

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).

Learn more about Confidence Interval here:

brainly.com/question/34700241

#SPJ6

A truck can be rented from Company A for $130 a day plus $0.50 per mile. Company B charges $50 a day plus $0.70 per mile to rent the same truck. How many milesmust be driven in a day to make the rental cost for Company A a better deal than Company B's?
For Company A to have a better deal, the truck must be driven more than miles per day

Answers

Answer:

200 miles

Step-by-step explanation:

hope this helps :)

Answer:

The charges of both companies will be same if truck is driven 200 miles per day

Company A will have better deal if truck is driven more than 200 miles per day ( because per mile rate of company A is less than company B

Step-by-step explanation:

Let the truck is driven X miles per day

Charges of company A will be = 90+0.4X

Charges of company B will be =30+0.7X

Let us find out value of X when charges of both companies are same

which means that 90+0.4 X= 30+0.7X

90-30 = 0.7X-0.4X

60 = 0.3X

60/0.3 = X

X= 200

Which function is a quadratic function?P(x)=2x(×^2+6)+1
M(x)=-4(x+3)-2
t(x)=-8x^2(x^2-6+1
H(x)=3x(x-2)-4

Answers

The correct answer is: [D]: " H(x) = 3x(x - 2) - 4 " .
__________________________________________________
Note: A "quadratic function" takes the form of:
__________________________________________________
f(x) = ax² + bx + c ;
_________________________________________________
Answer choice: [D]: " H(x) = 3x(x - 2) - 4 " ;

takes this form:
_________________________________________________
" H(x) = 3x(x - 2) - 4 " ;

→ " 3x(x - 2) - 4 " ;

Note the "distributive property" of multiplication:
_________________________________________________

a(b + c) = ab + ac ; AND

a(b - c) = ab - ac ;
_________________________________________________

→ As such;

" 3x(x - 2) = (3x * x) - (3x * 2) = 3x² - 6x;

So, we can rewrite the expression:

→ " 3x(x - 2) - 4 " ;

as: → " 3x² - 6x - 4 ;

And the entire function as:

H(x) = 3x(x - 2) - 4 ;

as:

H(x) = 3x² - 6x - 4 ;

Which takes the form of a "quadratic function" ;

→ f(x) = ax² + bx + c ;

in which: a = 3 ; b = - 6 ; c = - 4 .
____________________________________________________

Give brianliest and 15 points

Answers

Answer:

The correct answer is C

Step-by-step explanation:

X+U= [-1, -1] on the top and [0, -23/4] on the bottom

Therefore A-(X+U) gives you [5/3, 7] on the top and [4, 5] on the bottom

Hope this helps! :)

Answer:

Danke Shun!!!!!

Step-by-step explanation:

Oh mein Gott, danke für die kostenlosen Punkte, Kumpel !!

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