MATHEMATICS COLLEGE

TV advertising agencies face growing challenges in reaching audience members because viewing TV programs via digital streaming is increasingly popular. the Harris poll reported on November 13, 2012, that 53% of 2343 American adults surveyed said they have watched digitally streamed TV programming on some type of device.a. calculate and interpret a confidence interval at the 99% confidence level for the proportion of all adult americans who have watched streamed programming.b. what sample size would be required for the width of a 99% CI to be at most .05 irrespective of the value of p?

Answers

Answer 1

Answer:

Answer:

a) The 99% confidence interval would be given (0.503;0.557).

We are 99% confident that this interval contains the true population proportion.

b) $n=(0.53(1-0.53))/(((0.05)/(2.58))^2)=663.2$

And rounded up we have that n=664

Step-by-step explanation:

Data given and notation

n=2343 represent the random sample taken

X represent the people that they have watched digitally streamed TV programming on some type of device

$\hat p=0.53$ estimated proportion of people that they have watched digitally streamed TV programming on some type of device

$\alpha=0.01$ represent the significance level

Confidence =0.99 or 99%

z would represent the statistic for the confidence interval

p= population proportion of people that they have watched digitally streamed TV programming on some type of device

The population proportion present the following distribution:

$p \sim N (p, \sqrt{(p(1-p))/(n)}$

Part a) Confidence interval

The confidence interval would be given by this formula

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

For the 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_(\alpha/2)=2.58$

And replacing into the confidence interval formula we got:

$0.53 - 2.58 \sqrt{(0.53(1-0.53))/(2343)}=0.503$

$0.53 + 2.58 \sqrt{(0.53(1-0.53))/(2343)}=0.557$

And the 99% confidence interval would be given (0.503;0.557).

We are 99% confident that this interval contains the true population proportion.

Part b) What sample size would be required for the width of a 99% CI to be at most 0.05 irrespective of the value of p??

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

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

And on this case we have that $ME =\pm 0.05$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\hat p (1-\hat p))/(((ME)/(z))^2)$ (b)

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

$n=(0.53(1-0.53))/(((0.05)/(2.58))^2)=663.2$

And rounded up we have that n=664

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What is 160 divided by 18

Answers

Answer:

80/9 or 8.8888...

Step-by-step explanation:

Answer:

8.88888888889

160 divided by 18 is 8.88888888889.

Short for 8.889

The length of a side of a triangle is 36. A line parallel to that side divides the triangle into two parts of equal area. Find the length of the segment determined by the points of intersection between the line and the other two sides of the triangle

Answers

Answer:

18√2

Step-by-step explanation:

The area of the smaller triangle is 1/2 that of the larger one. Since the triangles are similar, the dimensions of the smaller triangle are √(1/2) those of the larger one.

36 · √(1/2) = 36 · (√2)/2 = 18√2 . . . . length of line dividing the triangle

Which relation is a function?

Answers

Answer:

the third one cause of it's inputs

A sphere that has a diameter of 6 what is the volume of the sphere

Answers

Answer:

36 pi or 113.04

Step-by-step explanation:

The volume of a sphere is given by

V= 4/3 pi r^3

we know the diameter so we need to find the radius

r =d/2

r = 6/2 = 3

V = 4/3 pi (3)^3

V =36 pi

We can approximate pi by 3.14

V is approximately 36 *3.14 or 113.04

Answer:

113.1 (113.0973355...)

Step-by-step explanation:

1. Use the sphere volume formula of $(4)/(3)$ π $r^(3)$ .

2. Divide 6 by 2 in order to get a radius of 3.

3. Substitute 3 in for r.

4. Cube the 3, you'll get 27.

5. Multiply 27 by Pi and 4/3.

6. You get 113.1 as a rough estimate, or 113.0973355... for a more exact number. If you leave it in Pi terms, it's 36π.

For the 405 highway that car pass through a checkpoint, assume the speeds are normally distributed such that μ= 61 miles per hour and δ=4 miles per hour. Calculate the Z value for the next car that passes through the checkpoint will be traveling slower than 65 miles per hour.

Answers

Answer:

$Z = 1$

Step-by-step explanation:

Z - score

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 61, \sigma = 4$

Calculate the Z value for the next car that passes through the checkpoint will be traveling slower than 65 miles per hour.

This is Z when X = 65. So

$Z = (X - \mu)/(\sigma)$

$Z = (65 - 61)/(4)$

$Z = 1$

I need a reason how sort from least to greatest I don’t understand

Answers

Answer:

Step-by-step explanation:

$√(9) < 3.758375839203... < √(16) \n\n(√(20) )/(4) =\sqrt{(20)/(16) }=√(1.25) \n\n3√(2) =√(18) \n\n\n1.25 < 9 < 16 < 18 < 22\n\n\n\Rightarrow\ \ (√(20) )/(4) < 3.758375839203... < 3√(2) < √(22)$

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