Suppose that prior to conducting a coin-flipping experiment, we suspect that the coin is fair. How many times would we have to flip the coin in order to obtain a 96.5% confidence interval of width of at most .12 for the probability of flipping a head

Answers

Answer 1

Answer:

We have to flip the coin 78 times.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

We suspect that the coin is fair.

This means that [tex]\pi = 0.5[/tex]

96.5% confidence level

So [tex]\alpha = 0.035[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.035}{2} = 0.9825[/tex], so [tex]Z = 2.108[/tex].

How many times would we have to flip the coin in order to obtain a 96.5% confidence interval of width of at most .12 for the probability of flipping a head?

n times, and n is found when M = 0.12. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.12 = 2.108\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.12\sqrt{n} = 2.108*0.5[/tex]

[tex]\sqrt{n} = \frac{2.108*0.5}{0.12}[/tex]

[tex](\sqrt{n})^2 = (\frac{2.108*0.5}{0.12})^2[/tex]

[tex]n = 77.1[/tex]

Rounding up

We have to flip the coin 78 times.


Related Questions

According to the AAA Foundation for Traffic Safety's American Driving Survey, U.S. drivers spend.

on average, 51 minutes behind the wheel each day. A researcher believes this is an overstatement.

To investigate, a random sample of 75 drivers were selected. The study revealed that the mean

time behind the wheel for the sample of 75 drivers was 46.4 minutes with a standard deviation of

18.8 minutes. Is there convincing evidence that the mean time behind the wheel for all U.S. drivers

is less than 51 minutes? Use a = 0.01.

Answers

Answer:

The pvalue of the test is 0.017 > 0.01, which means that there is not convincing evidence that the mean time behind the whell for all U.S drivers is less than 51 minutes.

Step-by-step explanation:

U.S. drivers spend on average, 51 minutes behind the wheel each day.

This means that at the null hypothesis we test that:

[tex]H_{0}: \mu = 51[/tex]

Is there convincing evidence that the mean time behind the wheel for all U.S. drivers is less than 51 minutes?

This means that the alternate hypothesis is:

[tex]H_{a}: \mu < 51[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

51 is tested at the null hypothesis:

This means that [tex]\mu = 51[/tex]

The study revealed that the mean time behind the wheel for the sample of 75 drivers was 46.4 minutes with a standard deviation of 18.8 minutes.

This means that [tex]n = 75, X = 46.4, \sigma = 18.8[/tex]

Value of the test-statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{46.4 - 51}{\frac{18.8}{\sqrt{75}}}[/tex]

[tex]z = -2.12[/tex]

Pvalue of the test:

The pvalue of the test is the probability of finding a sample mean less than 46.4, which is the pvalue of z when X = 46.4.

Looking at the z-table, z = -2.12 has a pvalue of 0.017.

Decision:

The pvalue of the test is 0.017 > 0.01, which means that there is not convincing evidence that the mean time behind the whell for all U.S drivers is less than 51 minutes.

No, there isn't convincing evidence that the mean time behind the wheel for all U.S. drivers is less than 51 minutes.

Given the following data:

Mean = 51.Number of drivers = 75 drivers.Sample mean (mean time) = 46.4 minutes.Standard deviation = 18.8 minutes.

What is a null hypothesis?

A null hypothesis ([tex]H_0[/tex]) can be defined the opposite of an alternate hypothesis ([tex]H_a[/tex]) and it asserts that two (2) possibilities are the same.

For the null hypothesis, we would test that:

[tex]H_o : \mu =51[/tex]

For the alternate hypothesis, we would test that:

[tex]H_a : \mu < 51[/tex]

The test statistics would be calculated with this formula:

[tex]Z=\frac{x\;-\;u}{\frac{\delta}{\sqrt{n} } }[/tex]

Where:

x is the sample mean.u is the mean.[tex]\delta[/tex] is the standard deviation.n is the number of drivers.

Substituting the given parameters into the formula, we have;

[tex]Z=\frac{46.4\;-\;51}{\frac{18.8}{\sqrt{75} } }\\\\Z=\frac{-4.6}{\frac{18.8}{8.6603} }\\\\Z=\frac{-4.6}{2.1708 }[/tex]

Z = -2.12.

What is a p-value?

In Statistics, a p-value also known as the probability value is the probability which occurs when the null hypothesis ([tex]H_0[/tex]) is true of obtaining a sample mean that is at least as unlikely as what is observed by a researcher or scientist.

From the z-table, a z-score of -2.12 corresponds to or has a p-value of 0.017. Therefore, the p-value for this test is 0.017 > 0.01.

In conclusion, there isn't convincing evidence that the mean time behind the wheel for all U.S. drivers is less than 51 minutes.

Read more on null hypothesis here: https://brainly.com/question/14913351

Use the point-slope form to write an equation of a line through the given points.
(−3, 2) and (3, 4)

Answers

Answer:

y-2=1/3(x+3)

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(4-2)/(3-(-3))

m=2/(3+3)

m=2/6

simplify

m=1/3

y-y1=m(x-x1)

y-2=1/3(x-(-3))

y-2=1/3(x+3)

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 410 gram setting. It is believed that the machine is underfilling the bags. A 22 bag sample had a mean of 408 grams with a standard deviation of 14. A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the bags are underfilled

Answers

Answer:

i think it is 451 i believe

Show
that (2+√3)(2-√3)(5+root2)
(5-root2) is rational number.​

Answers

Answer:

(2+3)(2−3)(5+2)(5−2)=>(22−(3)2)(52−(22))=>(4−3)(25−2)=>(1)(23)=>23

(2+√3)(2-√3)(5+ √2)
(5-√2)=(2^2-√3^2)(5^2-√2^2)=(4-3)(25-2)=23 and 23 is rational number

In ΔKLM, m = 480 cm, k = 360 cm and ∠L=29°. Find the area of ΔKLM, to the nearest square centimeter.

Answers

Answer:

The answer is=

41887.551


What should be included in a financial plan to protect assets?

Answers

The answer is how much insurance you will carry.

300 paper cups in a dispenser the cups are taken from dispenser at rate at rate of 40 cups per hour

Answers

Answer:

i dont know i dont understand the question

Which property can be used to solve the equation?
d/10=12

A. addition property of equality
B. subtraction property of equality
C. multiplication property of equality
D. division property of equality

Answers

Answer:

C

Step-by-step explanation:

You are dividing, if you think about it every time I do it is the opposite of your equation. Plus you are supposed to multiply on both sides to get the value of d.

What is the perimeter of the shaded part of this??

Answers

Answer:

18.9cm ( I rounded of and used Π as 3.14)

Step-by-step explanation:

P=distance all round

=1\2ΠD +Πd

see you have to calculate the upper length of the circle , since its half u multiply by a half. And since its not fully shaded the two semi circles are now included as the lower part of the whole shape. so you add them too. (I hope I'm making sense)

Reflect (2.5,4.5)​ in the x-axis.

Answers

9514 1404 393

Answer:

  (2.5, -4.5)

Step-by-step explanation:

Reflection in the x-axis changes the sign of the y-coordinate

  (x, y) ⇒ (x, -y)

  (2.5, 4.5) ⇒ (2.5, -4.5)

12. Find the measure of angle x.

13. Find the measure of angle x.

Answers

Answer:

x=21

x=122

Step-by-step explanation:

Answer:

x= 21

x=122

I hope this will help you.

PLEASE HURRY
A public radio station raised 25% more during this year's fund-
raiser than it raised last year. If p represents the amount raised
by last year's fund-raiser, which expression represents the
amount raised this year?

Answers

Answer:

1.25p

Step-by-step explanation:

p = amount raised last year

amount raised this year = p +(25% of p)

=1 p+0.25p

=p(1+0.25)

=1.25p

Which of the following is the measure of an acute angle?
A. 89°
B. 270°
C. 97°
D. 122°

Answers

Answer:

A

Step-by-step explanation:

An acute angle is an angle that is less than 90 degrees.

Answer:

Step-by-step explanation:

A

what is the equation for the volume of a cylinder? I think is v=pi × r^2 * h just asking for clarification ​

Answers

Answer:

V=pi multiplied by r^2 times height

Step-by-step explanation:

Is 2/9 a perfect square

Answers

ummm yes i think so. correct me if wrong

Hall and rey are seeing who can make the most money working their new summer jobs. Rey made $154.21 in the first month. If hall finishes the summer with $313.06, how many hours at a rate of $8.04 per our, does rey need to work to make more than hall
Write an inequality that represents the situation using x to represent the hours

Answers

Answer:

x564.99

Step-by-step explanation:

PLEASE HELP!!!!!! I WILL MARK YOU BRAINIEST

Answers

Answer:

Measure of angle b is 42 degrees

Step-by-step explanation:

Since angle b is part of a right angle, we can see that part of the right and blue is 48 degrees, and the other part is b. So, we can do 90-48 to get 42 degrees.

Answer:

42

Step-by-step explanation:

since one of the lines for angle b makes a 90° angle all you have to do is subtract 48 from 90 and that is your answer

Type the correct answer in the box log's​

Answers

Answer:

log(7) will be the correct answer.

Step-by-step explanation:

[tex]\text{\frac{14}{3}}+\text{log}(\frac{11}{5})-\text{log}(\frac{22}{15})[/tex]By using law of logarithm to solve the given expression,

1). [tex]\text{log}(m)+\text{log}(n)=\text{log(mn)}[/tex]

2). [tex]\text{log(m)}-\text{log(n)}=\text{log}(\frac{m}{n})[/tex]

By applying these rules, we can simplify the given expression,

[tex]\text{log}(\frac{14}{3})+\text{log}(\frac{11}{5})-\text{log}(\frac{22}{15})[/tex]

[tex]\text{log}(\frac{14}{3})+\text{log}(\frac{11}{5})-\text{log}(\frac{22}{15})=\text{log}(\frac{\frac{14}{3}\times \frac{11}{5}}{\frac{22}{15}})[/tex]

                                          [tex]=\text{log}(\frac{\frac{154}{15}}{\frac{22}{15}})[/tex]

                                          = [tex]\text{log}(\frac{154}{15}\times \frac{15}{22})[/tex]

                                          = log(7)

Therefore, log(7) will be the correct answer.

In the book Chances: risk and odds in Everyday Life, author James Burke says that approximately 57% of the general US population wears glasses or contacts. If two people are chosen at random from the US population, what is the probability that both wear glasses or contacts?

Answers

Answer:

[tex]Pr = 32.49\%[/tex]

Step-by-step explanation:

Given

Let E represents the event of wearing glasses or contacts.

So;

[tex]P(E) =57\%[/tex]

Required

The probability that selected 2 wears glasses

This is calculated as:

[tex]Pr = P(E)\ and\ P(E)[/tex]

[tex]Pr = P(E)\ *\ P(E)[/tex]

[tex]Pr = 57\% * 57\%[/tex]

[tex]Pr = 0.57 * 0.57[/tex]

[tex]Pr = 0.3249[/tex]

[tex]Pr = 32.49\%[/tex]

What is the solution to the equation?
19 + 13x = 32
Record your answer in the boxes
below.
00000.00
+/-
I give brainleist

Answers

Answer:

the answer is x=1

Step-by-step explanation:

minus 19 on both sides

then divide by 13 on both sides

Mike, Tania, Bill, and Rachael each took many samples from the same
population of students. The number of students in each sample is shown in
the table. Which person's sampling distribution is most likely to closely
approximate the population distribution?
Person taking samples Students in each sample
Mike
79
Tania
23
Bill
37
Rachael
51
A. Tania
B. Mike
C. Bill
D. Rachael

Answers

Answer: Mike!

Step-by-step explanation:

How is the graph of the parent quadratic function transformed to produce the graph of y--(2x+6)2+3?
O The graph is compressed horizontally by a factor of 2, shifted left 3 units, reflected over the x-axis, and translated
up 3 units
O The graph is reflected over the x-axis, compressed horizontally by a factor of 2, shifted left 6 units, and translated
up 3 units
The graph is stretched horizontally by a factor of 2, reflected over the x-axis, shifted left 3 units, and translated up
3 units
O The graph is reflected over the x axis, stretched horizontally by a factor of 2, shifted left 6 units, and translated up
3 units

Answers

Answer: a

Step-by-step explanation:

just took the test

solve it : x² *dy/dx = -2y

Answers

Answer:

r= -sec(θ) x ∛2

θ=0

Step-by-step explanation:

A container has a volume of 3.6 m3 . Convert the volume into cm3 .

Answers

Answer: 3 600 000 cm³

Step-by-step explanation: 1 m³ = 1000 dm³ = 1 000 000 cm³

1 = 5cm base s = 8cm s= 8cm 1 = q cm


what is surface area​

Answers

Answer:

The surface of the area is 320 cm. :D

Step-by-step explanation:

max is a 22 year old planning to retire at age 67 he is i vesting in a mutual fund and hopes to earn the average inflation adjusted stock market return of 7% anually. If max deposits $200 per month into this fund, how much can he expect to have when he retires? Show work

Answers

Based on the calculation below, the amount Max can be expected to have when he retires is $758,518.94.

How to calculate the future value (FV)?

The amount he will be expected to have when he retires can be calculated using the formula for calculating the future value of an ordinary annuity as follows:

FV = D * (((1 + r)^n – 1) / r) ……………………………….. (1)

Where;

FV = Future value or the expected amount when he retires = ?

D = Monthly deposit = $200

r = monthly average inflation adjusted stock market return = 7% / 12 = 0.07 / 12 = 0.00583333333333333

n = number of months = (67 -  22) * 12 = 540

Substituting the values into equation (1), we have:

FV = $200 * (((1 + 0.00583333333333333)^540 – 1) / 0.00583333333333333)

FV = $758,518.94

Learn more about future value here: https://brainly.com/question/14586629.

#SPJ1

Need ASAP


Gabe spent 26 days traveling in Europe. How many hours did he spend traveling in Europe?

Answers

Answer:

624hours

Step-by-step explanation:

There are 24 hours in a day, so multiply the amount of days by 24 to find the amount of hours:

26 x 24 = 624hours

Which expressions are equivalent to 16^(3/2)?

Answers

Answer:

16^(3/2)=64

Step-by-step explanation:

5/x=7/x-4
pls help me with this problem if u help i willl heart and follow you​

Answers

Answer:

5/x = 7/x-4

5(x-4) = 7(x)

5x - 20 = 7x

5x - 7x = 20

-2x = 20

x = -20/2 = -10

What is the product of 2.416 and 10^5​? *

Answers

ANSWER:

2.416x10^5

Or

241600

Both are correct the second is just in expanded form


MARK ME BRAINLIEST PLEASE

Answer:

241600

Step-by-step explanation:

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