Two sisters, sister A and sister B, play SCRABBLE with each other every evening. Sister A is a statistician, and she draws a random sample of 30 results from the 1,420 total games that have been played to construct a confidence interval estimate of p, the proportion of SCRABBLE games between her and her sister that she has won. Her 95% confidence interval estimate of p is LCL = 0.36, UCL = 0.69.

A 95% confidence interval estimate of the total number of games sister A has won out of the 1,450 games that have been played is LCL =___________ and UCL = ___________

The Illinois State Toll Highway Authority is conducting a study to estimate the proportion of low-income commuters who drive to work on a toll road. The project manager wants to estimate the proportion to within 0.03 with 95% confidence, and the project manager believes that p will turn out to be approximately 0.11.

A sample size no smaller than __________ is needed.

Answers

Answer 1

Answer:

First question: LCL = 522, UCL = 1000.5

Second question: A sample size no smaller than 418 is needed.

Step-by-step explanation:

First question:

Lower bound:

0.36 of 1450. So

0.36*1450 = 522

Upper bound:

0.69 of 1450. So

0.69*1450 = 1000.5

LCL = 522, UCL = 1000.5

Second question:

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]

The project manager believes that p will turn out to be approximately 0.11.

This means that [tex]\pi = 0.11[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The project manager wants to estimate the proportion to within 0.03

This means that the sample size needed is given by n, and n is found when M = 0.03. So

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

[tex]0.03 = 1.96\sqrt{\frac{0.11*0.89}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.96\sqrt{0.11*0.89}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.11*0.89}}{0.03}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{0.11*0.89}}{0.03})^2[/tex]

[tex]n = 417.9[/tex]

Rounding up

A sample size no smaller than 418 is needed.


Related Questions

mobymax help 11 points math

Answers

Answer:

10/15 + 3/15 = 13/15

Step-by-step explanation:

10/15 + 3/15 = 13/15

You are standing 6 feet away from the stage and your friend is standing 7 feet away from the stage.

Answers

Answer:

Step-by-step explanation:

Yo diría que Messi

Solve for u.
127-u = 258
24 =
What is u?

Answers

127 - u = 258

-u = 258 - 127

-u = 131 | : (-1)

u = -131

Answer:

127-u=258

258-127=131

12 = 0.005 X W
Solve the equation

Answers

Please mark me brainliest!!!

The answer is W= 2400 bc you have to divide both sides.

Hope this helps!

Answer: look at the picture

Step-by-step explanation: Hope this help :D

Which expression has a value of 252?

Answers

Step-by-step explanation:

6^3+6^2=216+36=252

25^2=625

hope that helps :)

Answer:

6^3 + 6^2

Step-by-step explanation:

6^3+6^2=216+36=252

25^2=625

625≠252

Hope this helps =]

how do you find the percent of discount if the original price is $578 and the sale price is $78.76

Answers

Answer: 86%discount approx

Step-by-step explanation:

You need to think about how the original price (578) is 100% of the price and that the sale price (78) is just a percentage of that. To discover how much of that 100% the price 78 is, you can write the formula:

578:100=78:x

X=(78*100)/578

X=14 %

Once you know that 78 represents the 14% of the whole price (100%-578) you just have to subtract that amount from the whole to understand which percent of discount has been applied: 100-14 = 86%

Which step in the proof has a flow?

1.Statement 2
2.Reason 3
3.statement 3
4.Reason 2

Answers

Answer:

Reason 2

Step-by-step explanation:

The reason should be transitive property( if a=b and b=c then a=c) not reflective property.

q is a degree 5 polynomial that passes through the origin, has zeros i and 3 - i, and q( - 2) = - 520. Find
the equation for g.
User for your input. Simplify your answer so that it has only real numbers as coefficients.

Answers

Keirekwkwmsndnsnwowooskssk

Which expression is equivalent to 5 (4x+3)-2

Answers

Simplifying Expressions

To simplify an expression means to write it in the simplest way possible. Ideally, there would be no parentheses and everything has been 'expanded'.

Solving the Question

We're given:

[tex]5 (4x+3)-2[/tex]

[tex]5 (4x+3)-2[/tex]

Open up the parentheses by multiplying each term by 5:

[tex]=5*4x+5*3-2\\=20x+15-2\\=20x+13[/tex]

Answer

[tex]20x+13[/tex]

Muhammad spent $45 buying three pizzas and two orders of wings for his roommates. Each pizza cost twice as much as the wings +1 dollar what does one order of wings cost?

Answers

MARK BRAINLIEST SO I CAN LEVEL UP
so I did $45 divided by 3 and got $15 I then divided $15 by 2 since the cost of one pizza is the cost of the wings plus $1 so you get $7.50 so you add $7.50 plus 1 and you get $8.50 therefore one order of wings in $8.50

Which expression has the least value when x = 100?

A.
1
x

B.
10
x

C.
1

x

D.
10

x

Answers

Answer:

Hi! The answer to your question is B. [tex]10x[/tex]

Step-by-step explanation:

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☆Brainliest is greatly appreciated!☆

Hope this helps!!

- Brooklynn Deka

PLZ HELP ASAP
Ps I accidently clicked on a choice

Answers

I’m almost 100% sure that it’s the option directly above the one that you chose

Answer:

B or top right answer or second answer is correct.

Find the value of x for the right triangle.
45°
х
10

Answers

Answer:

14.14

Step-by-step explanation:

sin(45)=10/x. <--fraction

then solve for x you should get this

x=10/sin(45)

and that should equal

14.14213562

Marina will attend choir practice for 2-
hours on Saturday, 24 hours on Sunday,
and 3 hours on Monday. Next week,
Marina will attend choir practice for the
same number of hours on Saturday,
Sunday, and Monday.
What is the total number of hours
Marina will have choir practice over
these 6 days?

Answers

Answer:

58

Step-by-step explanation:

1).2+24+3 = 29

2) 29 x 2 = 58

Find the slope of the line represented
by the data below.

Answers

Answer:

slope = 3/4

Step-by-step explanation:

(=^w^=)

can do 7-4/-5--9

3/4 woof

The slope of the line represented by the given data points is 3/4.

To find the slope of the line represented by the given data points, we can use the formula for slope:

slope = (change in y) / (change in x)

Let's calculate the changes in y and x using the given data points:

Change in y:

From y = 4 to y = 16, there is an increase of 16 - 4 = 12.

Change in x:

From x = -9 to x = 7, there is an increase of 7 - (-9) = 16.

Now, we can calculate the slope using the formula:

slope = (change in y) / (change in x)

= 12 / 16

= 3 / 4

Therefore, the slope of the line represented by the given data points is 3/4.

To know more about slope click here :

https://brainly.com/question/14511992

#SPJ2

Mr. Nelson sold a car for $1,380 that cost
him $1,500. What was his percent of loss
based on the cost?​

Answers

Answer:

The loss is $120 and the loss percentage is 8%.

Step-by-step explanation:

Given that,

SP of a car = $1,380

CP of a car = $1,500

As CP > SP, it means there is a loss in selling of that car.

Loss = CP - SP

= $1,500 - $1,380

= $120

Loss percentage,

[tex]\%=\dfrac{loss}{CP}\times 100\\\\=\dfrac{120}{1500}\times 100\\\\=8\%[/tex]

Hence, the loss is $120 and the loss percentage is 8%.

2 friends equally share 5 cookies. How many cookies
does each friend get?​

Answers

They both get 2 and 1/2 of a cookie!

Answer:

2 1/2

Step-by-step explanation:

The only way for the friends to get an equal amount is to split one of the cookies in half. or 5 divided by 2= 2 1/2

2x+5+(6x+1)

Help please.

Answers

Answer:

14x

Step-by-step explanation:

The (6x+1) = 7 and the other equation also equals 7 so you add together and just ad the x variable since there is no answer

help please i genuinely cant

Answers

Answer:

Part A: 3x + 36 = 180

Part B: x = 48

Step-by-step explanation:

A straight line is equal to 180 degrees. Knowing this, both 3x and 36 should be equal to 180. Write an equation:

3x + 36 = 180

Solve the equation:

3x + 36 = 180

Subtract 36 from both sides

3x = 144

Divide both sides by 3 to isolate the variable

x = 48

Check your work:

3(48) + 36 = 180

144 + 36 = 180

180 = 180

Correct

Write an equation of the line below.

Answers

Answer (assuming it can be in slope-intercept form):

[tex]y = \frac{4}{5} x[/tex]

Step-by-step explanation:

1) First, find the slope of the line. Use the slope formula [tex]m = \frac{y_2-y_1 }{x_2-x_1}[/tex] and substitute the x and y values of two points on the line into it. We can see that the line passes through (0,0) and (5,4), so let's use those points for the formula and solve:

[tex]m = \frac{4-0}{5-0} \\m = \frac{4}{5}[/tex]

So, the slope is [tex]\frac{4}{5}[/tex].

2) Next, identify the y-intercept of the line. The y-intercept is the point at which the line intersects the y-axis. We can see that the line intersects the y-axis at (0,0), so that must be the y-intercept.

3) Now, write the equation of the line in slope-intercept form using the [tex]y = mx + b[/tex] format. The number in place of [tex]m[/tex] represents the slope, so substitute [tex]\frac{4}{5}[/tex] in its place. The number in place of [tex]b[/tex] represents the y-intercept, so substitute 0 in its place. This gives the following answer and equation:

[tex]y =\frac{4}{5} x+0\\y = \frac{4}{5} x[/tex]

Answer:

y=4/5x

Step-by-step explanation:

y=mx+b where m=slope and b=y-intercept

In this problem, the slope is 4/5 because m=rise/run.

What time is it in iowa when the sun goes down in new york at 5:20 pm est?

Answers

It will be 4:20 pm in Iowa Eastern time to Central Time

kimtoya travels from New York to Florida by airplane. She pays a total of $402 for her flight. This includes a base price of $285 for the ticket plus a fee for each of her 3 pieces of checked baggage. To figure out how much the fee per bag is, she adds $402 to $285 and then divides this total by 3 to get $173. Is Kimtoya correct? Include all necessary work to support your answer.​

Answers

Answer:

402

+285

687÷3=229

Step-by-step explanation:

so nah she's not right

A study9 compared personality characteristics between adult children of alcoholics and a control group matched on age and gender. For the 29 pairs of women, the authors reported a mean of 24.8 on the well-being measure for the children of alcoholics, and a mean of 29.0 for the control group. They reported t = 2.67 for the test comparing the means. Assuming that this is the result of a dependent-samples analysis, identify the df for the t test statistic, report the P-value, and interpret.

Answers

Answer:

df.= 28

P - value = 0.0124 < 0.05

There is a difference between the mean of  the well-being measure for the children of alcoholics, and a mean of the control group.

Step-by-step explanation:

As the given test is dependent or paired test the degrees of freedom is n-1 = 20-1 = 28

The reported t = 2.67

The P value for ∝= 0.05 at  calculated t= 2.67 and 28 d.f is 0.0124 which is less than 0.05 .

The null hypothesis is rejected.

The null hypothesis is that there is no difference between the means of the two samples.

H0: u1 = u2

The alternate hypotheis is accepted that there is  difference between the means of the two samples.

Ha: u1≠ u2

There is a difference between the mean of  the well-being measure for the children of alcoholics, and a mean of the control group.

Use the following image to multiply.
5/8 of 4 =

Answers

Answer:

2.5

Step-by-step explanation:

Answer:

[tex]2\frac{1}{2}[/tex] or 2.5

Step-by-step explanation:

[tex]\frac{5}{8}*4\\ \\ =\frac{5}{8}*\frac{4}{1} \\ \\ =\frac{5*4}{8*1} \\ \\ =\frac{20}{8} \\ \\ =\frac{5}{2} \\ \\ =2\frac{1}{2} or 2.5[/tex]

WILL GIVE BRAINLIST
What is the equation of the line that passes through the point (1, 3) and is perpendicular to the line 2x+3y=15?

Answers

Answer:

y = 3/2x + 3/2

Step-by-step explanation:

perpendicular to: y = -2/3x + 5

so slope of new line must be 3/2

y = mx + b

3 = 1(3/2) + b

6/2 = 3/2 + b

b = 3/2

https://brainly.com/question/23008046


PLS ANSWER THIS QUESTION PLEASE

Answers

Answer:

[tex]\frac{3}{2}y - 3 + \frac{5}{3}z =11[/tex]

Step-by-step explanation:

Given

[tex]y=6; z=3[/tex]

Evaluate

[tex]\frac{3}{2}y - 3 + \frac{5}{3}z[/tex]

Substitute [tex]y=6; z=3[/tex] in the expression.

So, we have:

[tex]\frac{3}{2}y - 3 + \frac{5}{3}z = \frac{3}{2}*6 - 3 + \frac{5}{3} * 3[/tex]

[tex]\frac{3}{2}y - 3 + \frac{5}{3}z = \frac{3*6}{2} - 3 + \frac{5* 3}{3}[/tex]

Evaluate the fractions

[tex]\frac{3}{2}y - 3 + \frac{5}{3}z = 3*3 - 3 + 5[/tex]

[tex]\frac{3}{2}y - 3 + \frac{5}{3}z =11[/tex]

What is one way to name the object pictured below?
A Z Y
B. YZ
c. Y Z
D. ZY

Answers

You got it correct the answer is B

MARK ME BRAINLIEST PLEASE

girlcome 5324611502
p:here​

Answers

Answer:

what

Step-by-step explanation:

Answer:

im confused

Step-by-step explanation:

someone actually help me please :/ I REALLY NEED HELP AND NO ONES HELPING

Answers

Answer:

a) 8 m  

Step-by-step explanation:

a) all sides of a square are equal - there's 4 sides.

4x = 32m

x = 32/4

x = 8 m

i like ur toga pfp besty :)



Julie runs 3 miles each morning. How far does she run in feet?
(1 mile = 5,280 feet)

Answers

Answer:

15,840 feet

Step-by-step explanation:

5,280*3 = 15840

Since she runs 3 miles each morning, and 1 mile is 5,280,

then you multiply 5,280*3

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