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saw5 [17]
3 years ago
14

Determine the sample size needed to construct a 90% confidence interval to estimate the population proportion when p = 0.65 and

the margin of error equals 6%.
Mathematics
1 answer:
WINSTONCH [101]3 years ago
6 0

Answer:

n=170

Step-by-step explanation:

1) Notation and definitions

n random sample taken (variable of interest)

\hat p=0.65 estimated proportion.

p true population

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by \alpha=1-0.90=0.1 and \alpha/2 =0.05. And the critical value would be given by:

z_{\alpha/2}=\pm 1.64

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

And on this case we have that ME =\pm 0.06 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

And replacing into equation (b) the values from part a we got:

n=\frac{0.65(1-0.65)}{(\frac{0.06}{1.64})^2}=169.968  

And rounded up we have that n=170

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Avery deposited $400 in an account that earned 2.47% interest compounded annually. She did not make additional deposits or withd
aev [14]

Answer:

Amount ($451.9), Interest ($51.9)

Step-by-step explanation:

We need to use the formula of A = P(1 + \frac{r}{n})^n*t

A = Total Amount

P = Principle/Deposited money

R = Annual Interest Rate

N = Number of times compounder per year

T = time in years

We have P = $400, r = 2.47%, n = 1 and t = 5 years.

Now lets plug it all in!

A = 400 (1 + \frac{0.0247}{1})^{1*5}

A = 400 * 1.0247^5

A = 400 * 1.129753

A = 451.9

Now we need to find the interest...

We will use A = P + I since A is 451.9 and P = 400

451.9 = 400 + I

I = 451.9 - 400

I = 51.9

6 0
2 years ago
What is the solution for x? 9-x/5=3
navik [9.2K]

Answer:

x = 30

Step-by-step explanation:

9-x/5=3

Subtract 9 from each side

9-9-x/5=3-9

-x/5 = -6

Multiply each side by -5

-x/5 *-5 = -6*-5

x = 30

8 0
3 years ago
Read 2 more answers
(72-y)+(26-X) when x=9,y=51
disa [49]

Answer:

38

Step-by-step explanation:

(72-51)+(26-9)

21+17

38

7 0
3 years ago
Two balls A and B rotate along a circular track. Ball A makes 4 full rotations in 120 seconds. Ball B makes 3 full rotation in 6
lara [203]
Find the rate in which both balls make one full rotation around the track.

Ball A:

120 / 4 = 30

It takes 30 seconds for Ball A to make a full rotation.

Ball B:

60 / 3 = 20

It takes 20 seconds for Ball B to make a full rotation.

Find the least common multiple of 20 and 30 to find the time at which they'll meet.

Multiples of 20: {20,40,60}
Multiples of 30: {30,60}

60 is the least common multiple of both 20 and 30.

The balls will meet again at 60 seconds.
5 0
3 years ago
The greatest common factor of 30.48.60
Elena-2011 [213]
30= 3*10
30= 3*2*5

48= 12*4
48= 3*4*4
48= 3*2*2*2*2

60= 3*20
60= 3*10*2
60= 3*2*5*2

The GCF is 3*2 because all 3 numbers contain a 3 and a 2 in their prime factorizations.

Final answer: 6
6 0
3 years ago
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