Mathematics College

A news article estimated that only 4% of those age 65 and older who prefer to watch the news, rather than to read or listen, watch the news online. This estimate was based on a survey of a large sample of adult Americans. Consider the population consisting of all adult Americans age 65 and older who prefer to watch the news, and suppose that for this population the actual proportion who prefer to watch online is 0.04. (a) A random sample of n = 100 people will be selected from this population and p, the proportion of people who prefer to watch online, will be calculated. What are the mean and standard deviation of the sampling distribution of p? (Round your standard deviation to four decimal places.) mean 0.04 standard deviation 0.0196 (b) Is the sampling distribution of p approximately normal for random samples of size n = 100? Explain. The sampling distribution of p is approximately normal because np is less than 10. O The sampling distribution of p is approximately normal because np is at least 10. The sampling distribution of p is not approximately normal because np is less than 10. The sampling distribution of p is not approximately normal because np is at least 10. The sampling distribution of is not approximately normal because n(1-P) is less than 10. (c) Suppose that the sample size is n = 400 rather than n = 100. What are the values for the mean and standard deviation when n = 400? (Round your standard deviation to four decimal places.) mean 0.03 standard deviation 0.0085 Does the change in sample size affect the mean and standard deviation of the sampling distribution of ? If not, explain why not. (Select all that apply.) 2 When the sample size increases, the mean increases. When the sample size increases, the mean decreases. When the sample size increases, the mean stays the same. The sampling distribution is always centered at the population mean, regardless of sample size. When the sample size increases, the standard deviation increases. When the sample size increases, the standard deviation decreases When the sample size increase the standard deviation stays the same. The standard deviation of the sampling distribution is always the same as the standard deviation of the population distribution regardless of sample size. Suppose that the sample size is n = 400 rather than n = 100. What are the values for the mean and standard deviation when n = 400? (Round your standard deviation to four decimal places.) mean 0.03 standard deviation 0.0085 Does the change in sample size affect the mean and standard deviation of the sampling distribution of p? If not, explain why not. (Select all that apply.) When the sample size increases, the mean increases. When the sample size increases, the mean decreases. When the sample size increases, the mean stays the same. The sampling distribution is always centered at the population mean, regardless of sample size. When the sample size increases, the standard deviation increases. When the sample size increases, the standard deviation decreases. When the sample size increases, the standard deviation stays the same. The standard deviation of the sampling distribution is always the same as the standard deviation of the population distribution, regardless of sample size. (d) is the sampling distribution of p approximately normal for random samples of size n = 400? Explain. The sampling distribution of p is approximately normal because np and n(1 - p) are both at least 10. The sampling distribution of p is approximately normal because np and n(1 - 0) are both less than 10. The sampling distribution of p is not approximately normal because np and n(i - p) are both at least 10. • The sampling distribution of p is not approximately normal because np and n(1-P) are both less than 10. The sampling distribution of p is not approximately normal because only np is at least 10.

Answers

Answer 1

Answer:

(a) The mean is 0.04

The standard deviation is approximately 0.0196

(b) The sampling distribution of p is not approximately normal because n·p is less than 10

(c) Given that n  = 400, we have;

i) The mean is 0.04

The standard deviation is approximately 0.0098

ii) The sampling distribution is always centered at the population mean, regardless of the sample size

iii) When the sample size increases, the standard deviation decreases

(d) The sampling distribution of p is approximately normal because n·p and n·(1 - p) are both at least 10

Step-by-step explanation:

(a) From the question, we have that the actual proportion of all adult Americans who watch online = 0.04

Given that the sample size, 'n' is 100 which is larger than 30, we can assume that the distribution of the sample mean is normal

Therefore, the mean (proportion) of the sample, P = The mean (proportion) of the population = 0.04

The mean, P = 0.04

The standard deviation, σ = √((p·(1 - p))/n)

∴ σ = √((0.04·(1 - 0.04))/100) ≈ 0.0196

(b) The sampling of p is approximately normal, given that the sample size, 'n' = 100 which is randomly selected from the population, we have;

The sampling distribution = n·p  = 100 × 0.04 = 4 <10

Therefore, the sample is not approximately normal because the sampling distribution, n·p = 4 which is less than 10

c) Given that n  = 400, we have;

p = 0.04 = The [population mean

The standard deviation, σ √((0.04·(1 - 0.04))/400) ≈ 0.0098

According to the central limit theorem when the sample size increases, the mean approaches the population mean, therefore, the sampling distribution is always centered at the population mean, regardless of the sample size

When the sample size increases, the standard deviation decreases

(d) Given that when the sample size, n = 400, we have;

n·p = 400 × 0.04 = 16 > 10

Similarly, we have;

n·(1 - p) = 400 × (1 - 0.04) = 384 > 10

The sample is approximately normal

Therefore, the sampling distribution of p is approximately normal because np and n(1 - p) are both at least 10

Related Questions

A survey of 2645 consumers by DDB Needham Worldwide of Chicago for public relations agency Porter/Novelli showed that how a company handles a crisis when at fault is one of the top influences in consumer buying decisions,with 73% claiming it is an influence. Quality of product was the number one influence, with 96% of consumers stating that quality influences their buying decisions. How a company handles complaints was number two, with 85% of consumers reporting it as an influence in their buying decisions. Suppose a random sample of 1,100 consumers is taken and each is asked which of these three factors influence their buying decisions.

Answers

Answer:

Step-by-step explanation:

The question that follows the passage include:

[tex]\text{a. What is the probability that more than 810 consumers claim that how a company } \\ \\ \text { handles a crisis when at fault is an influence in their buying decisions?}[/tex][tex]\text{b. What is the probability that fewer than 1,030 consumers claim that quality} \\ \\ \text{ of product is an influence in their buying decisions?}[/tex]

From the given information:

the sample size = 1100

P = 73% = 0.73

Sample proportion [tex]\hat p = \dfrac{810}{1100} = 0.7364[/tex]

The Z test statistics can be computed as:

[tex]Z = \dfrac{\hat p - p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]

[tex]Z = \dfrac{0.7364 - 0.73}{\sqrt{\dfrac{0.73(1-0.73)}{1100}}}[/tex]

[tex]Z = \dfrac{0.0064}{\sqrt{\dfrac{0.1971}{1100}}}[/tex]

[tex]Z =0.478[/tex]

a) Now the required probability of more than 810 claims is:

[tex]P(X> 810) = 1 - P(X<810) \\ \\ \implies 1 - ( X< 0.478) \\ \\ \implies 1 - 0.68367 \\ \\ = \mathbf{0.3163}[/tex]

b) The probability of less than 1030 consumers is:

Probability of quality product influencers = 96%  = 0.96

Sample proportion [tex]\hat p = \dfrac{1030}{1100}[/tex] = 0.9364

The Z test Statistics is:

[tex]Z = \dfrac{\hat p - p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]

[tex]Z = \dfrac{0.9364 - 0.96}{\sqrt{\dfrac{0.96(1-0.96)}{1100}}}[/tex]

[tex]Z = -3.994[/tex]

[tex]P(X < 1030) = 1 - P(3.99) \\ \\ \implies 1 - 0.99999669 \\ \\ \implies \mathbf{0.00003 }[/tex]

OMG?!?!?!!?! HELP!!!?!?!?! PLEASE !?!?!? Thanks to those who do :D <3
A pump can fill 1800KL tank in one hour. How long would it take to fill a 90 KL tank?

Answers

20 hours because 1800/90=20

Ocean waves are hitting a beach with a frequency of 0.100 Hz. Their average wavelength is 15.0 m. What is their average speed?

Answers

Answer:

7 mph or 11.27 kphe

Step-by-step explanation:

Im pretty sure pls give 5 stars

Hello, Can you please answer this.​

Answers

Answer:

Hey!

V = 1906.624 cm^3

SA= 922.56 cm^2

Step-by-step explanation:

The surface area of a cube = 6a2 where a is the length of the side of each edge of the cube. Put another way, since all sides of a cube are equal, a is just the lenght of one side of a cube.

Volume of a cube = side times side times side.

I need help with this problem please

Answers

Answer:

-9

Step-by-step explanation:

Remove parentheses.

9(−1)2−7

Subtract 77 from 22.

9(−1)−5

Rewrite the expression using the negative exponent rule b−n= 1/bn

91(−1)5

Raise −1 to the power of 5.

9(1/-1)

Divide 1 by −1.

9⋅−1

Multiply 9 by −1.

−9

Find the equation of the given line.

Find the equation of the line passing through
(5, 6) and (7, 9).

Answers

Answer:

y = 3/2x - 1.5

Step-by-step explanation:

m = y² - y¹ / x² - x¹

= 9 - 6 / 7 - 5

= 3/2

(5,6)

y = mx + c

6 = 3/2 (5) + c

6 = 7.5 + c

6 - 7.5 = c

c = -1.5

PLEASE HELP ME WITH QUESTION ONE AND EXPLAIN YOUR ANSWER PLEASE

Answers

Answer:

168 in³

Step-by-step explanation:

First, you get the area of the triangle - 1/2(7)(6)=21.  Then you multiply it by the height.  21x8=168

Answer:

Answer in explanation

Step-by-step explanation:

The formula for volume of a triangular shape is Volume = base x height x length / divided by 2

1. V = 7 ( base ) x 6 ( height ) x 8 ( length ) divided by 2 = 168in3 ( in cubed )

2. V = 5 ( base ) x 6 ( height ) x 3 ( length ) divided by 2 = 45in3 ( in cubed )

* make sure you put all your answers for volume in in3

I hope this helped, good luck!

Angle ABD is 90°
What is the measure of ZABC?
O A 360
O B. 54°
OC. 90°
OD. 126°
O E. 144º

Answers

It would be answer choice B, 54 degrees.
you would do 90-36 to get the measure of angle ABC.

the volume of a rectangular prism is 10 cubic feet. what could the dimensions of the prism be

Answers

We need 3 numbers that equal 10 when multiplied. 1, 5, and 2 are what come to mind for me.

1x5=5

5x2=10

---

hope it helps

Select which of the following biconditionals is true. (Check all that apply.)

a. If n is even, then 7n + 4 is even; if 7n + 4 is even, then n is even.
b. If n is odd, then 7n + 4 is odd; if 7n + 4 is odd, then n is odd.
c. If n is even, then 7n + 4 is even; if 7n + 4 is odd, then n is odd.
d. If n is odd, then 7n + 4 is even; if 7n + 4 is even, then n is odd.

Answers

Your answer would be b for this question hope I could help! That is because out of all these b is all odd in which it lines up

Find each angle measure. ( Diagrams are not drawn to scale.)​

Answers

Answer:

1-141

2-39

3-141

Step-by-step explanation:

180-39=141

1 and 3 look the same size and 2 looks the same as c (39°) so you jsut fill in for the letters

I'm pretty sure this is right

Impossible for me plz help. Also please insure that you write a let statement :)

Answers

Let x equal the amount of money he/she started with (The pronouns change in the question.)

1/3x + 1/5x = 32
We need a common denominator to add the fractions. We’ll use 15.
5/15x + 3/15x = 32
8/15x = 32
Multiply both sides by 15/8, or multiply by 15, then divide by 8, if that is easier to understand.
8x = 480
x = 60

He/she started with $60.

Let’s check the math:
1/3 of $60 is $20
1/5 of $60 is $12
$20 + $12 = $32.

Please let me know if you have any questions. I hope you have a good day.

Simone read online that the failure rate in Arizona for the first attempt of the written driver’s test is 60%. Simone thinks the Arizona rate is less than 60%. To investigate, she selects an SRS of 50 Arizona drivers and finds that 27 failed their first written driving test. To determine if this provides convincing evidence that the failure rate for Arizona is less than 60%, 200 trials of a simulation are conducted. Simone’s hypotheses are: H0: p = 60% and Ha: p < 60%, where p = the true proportion of Arizona drivers who fail the first attempt of the written driver’s test. Based on the results of the simulation, the estimated P-value of this test is 0.035. Using α = 0.01, what conclusion should Simone reach?


Because the P-value of 0.035 > α, Simone should reject H0. There is convincing evidence that the Arizona written driver’s test has a true first-attempt failure rate less than 60%.

Because the P-value of 0.035 > α, Simone should reject H0. There is not convincing evidence that the Arizona written driver’s test has a true first-attempt failure rate less than 60%.

60%.
Because the P-value of 0.035 > α, Simone should fail to reject H0. There is convincing evidence that the Arizona written driver’s test has a true first-attempt failure rate less than 60%.

Because the P-value of 0.035 > α, Simone should fail to reject H0. There is not convincing evidence that the Arizona written driver’s test has a true first-attempt failure rate less than 60%

Answers

Answer:

Its B

Step-by-step explanation:

edge 2021

6. Describe how we could conduct a simulation to decide whether a simple random sample from this population could produce a sample proportion like 0.55 if, in fact, only 50% of the population supports ban on smoking in cars when young children are present. Each trial represents Number of trials

Answers

Step-by-step explanation:

We have proportion p = 50/100 = 0.50

Probability of success = 1-0.50 = 0.50

To conduct simulation, let's assume experiment is to be done 10 times

1. Use binomial parameters n, number = 10, p = 0.50. we then get the necessary size of population To carry out the sampling.

2. We get a random sample and get the size of people who support an against smoking with kids in the car.

3. We repeat this process after drawing sample and also get the number of those in support of ban.

4. After getting n, we find proportion.

How many times was the number cube rolled

Answers

The ball was rolled 50 times.

6+4+8+12+10+10 = 50

Hope this helps; have a great day!

Please answer quick just super small explanation pls hurry quick for brainlessly answer

Answers

The correct answer is E.

Simplify the expression:
​P + 7p + 5p

P = ?

A. 13p
B. 13
C. 16p
D. 16

Answers

The answer Is A. 13p hope it helps

pls answer ill give brainliest

Answers

Answer:

15

Step-by-step explanation:

the angle is opposite to 60 so it is also 60

60-45 = 15

Hope this helps :)

Which word is an antonym of permit?

Answers

Answer:

What are the options? ban, forbid, prohibit, are some examples

Step-by-step explanation:

Answer:

prohibited

permit means to allow so you would need a word that means not allowed which is prohibited

Pls help Find the value for n try to use x/y Pls pls pls help il mark brainliest pls i really need help pls pls help

Answers

Answer:

coprs said the United of a group that had to take the first time and was not the first person in a while and

Step-by-step explanation:

. 3^2x+1 = 1 solve it​

Answers

Answer:

x= 0

Step-by-step explanation:

Which scatter plot shows the relationship
between the amount of gasoline in an
automobile's tank and the distance travelled
since the last fill-up?

Answers

Answer:

-0.04x +17.2

Step-by-step explanation:

Delia put I two bags of blocks in the left-side pan of a balance. Each bag has the
same number of blocks. After she adds 10 blocks to the right-side pan, the pans
hang evenly. How many blocks are in 1 bag?

Answers

I agree the top of me is correct :)

A study of drive-thru wait times for fast-food restaurants found that the average time spent Wendy's drive-thru was 138.5 seconds. Assume that drive-thru wait times are normally distributed with a standard deviation of 29 seconds, A Wendy's owner wants to give a free Frosty to customers who have an unusually long wait in the drive-thru.
The length of time the owner should choose so that only 0.75% of customers get a free Frosty i.e. only 0.75% wait longer than ________ seconds) is _________ seconds (give your answer to 2 decimal places).

Answers

Answer:

207.72 seconds.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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 p-value, we get the probability that the value of the measure is greater than X.

Mean waiting time of 138.5 seconds, standard deviation of 29 seconds.

This means that [tex]\mu = 138.5, \sigma = 29[/tex]

The length of time the owner should choose so that only 0.75% of customers get a free Frosty i.e. only 0.75% wait longer than

The 100 - 0.75 = 99.15th percentile, which is X when Z has a pvalue of 0.9915, so X when Z = 2.387.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]2.387 = \frac{X - 138.5}{29}[/tex]

[tex]X - 138.5 = 2.387*29[/tex]

[tex]X = 207.72[/tex]

So the answer is 207.72 seconds.

Your teacher is giving a test that is made up of 3 point questions and5 point questions the test is worth 100 points and has 28 questions how many 3 points questions are there ?

Answers

Answer:

I am thinking 8 amigo, i could be wrong, so please look it up, or try to think about how to do it

Step-by-step explanation:

I hope you have a blessed day!

HELP please correct answer please mathematics

Answers

Answer:

96 units^2

Step-by-step explanation:

(8*24)/2=96

3m=117 solve da equation

Answers

If you are solving for m then the answer is m=39
Divide both sides of the equation by
3

3m divide 3 +117 divid 3

Any expression divided by itself equals
1.
M=117 divid 3

Calculate the quotient

Answer should be M=39

Solve each equation below for the variable given.
134+ p =74 p =
25/8 + m = 7 1/8 m =

Answers

Answer: For the first one: P=-60

The second one: m=4

Step-by-step explanation:

134+p=74

You move to the right and you change the sign

Like this: p=74-134

Then you Calculate the difference

So p=-60 which is your answer

The second one: 25÷8+m=7 1/8

You divide the numbers like this:3.125m=7 1/8

Convert the mixed number into an improper fraction.. like this: 3.125+m=57/8

Move constant to the right and change the sign

Like this: m=57/8 - 3.125

Convert the decimal into a fraction

m=57/8-25/8

Then you Calculate the difference

So it will be m=4 which is your answer

Let me know if this helps

HELPPP PLEASE YOU’LL GET 10 POINTS

Answers

Answer:

angle y and angle x

Step-by-step explanation:

Y and X hope this helps

lame 《 Solve & Share A flash drive costs $24, including tax. A customer purchases 3 flash drives and pays the cashier $80. How much change should the cashier give back to the customer? Solve this problem any way you choose.​

Answers

Answer:

$8

Step-by-step explanation:

1 flashdrive = $24

3 flash drives x $24 = $7

$80 - $72 = $8

Other Questions
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