A market researcher would like to know how much time the average college student spends watching sports. Suppose he does a preliminary study based upon a sample of 25 college students. The mean amount of time spent watching sports, by those in the sample, is 90 minutes per day with a standard deviation of 15 minutes per day.
(a) Which of the following numbers gives the value of the point estimate?
a. 15.
b. 25.
c. 90.
d. 0.
e. 95.
(b) Using the information given above, calculate the margin of error (in minutes) of the point estimate. Assume we would like to estimate the population mean with 95% confidence.
(c) Suppose that the researcher is not content with the current margin of error. He would like the margin of error of the point estimate to be no more than 4 minutes with 95% confidence. The researcher is unwilling to trust that the sample standard deviation from his previous study accurately estimates the true population standard deviation. He does, however, know that college students tend to watch sports between 0 and 120 minutes per day. What is the minimum sample size needed to obtain this amount of precision?

Answers

Answer 1

Answer:

a)  c. 90.

b) The margin of error of the point estimate is of 6.19 minutes.

c) The minimum sample size needed to obtain this amount of precision is 289.

Step-by-step explanation:

(a) Which of the following numbers gives the value of the point estimate?

The value of the point estimate is the sample mean, of 90 minutes. So the answer is given by option c.

(b) Using the information given above, calculate the margin of error (in minutes) of the point estimate. Assume we would like to estimate the population mean with 95% confidence.

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 25 - 1 = 24

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0639.

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}}[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

Here, we have [tex]s = 15, n = 25[/tex]. So

[tex]M = T\frac{s}{\sqrt{n}}[/tex]

[tex]M = 2.0639\frac{15}{\sqrt{25}}[/tex]

[tex]M = 6.19[/tex]

The margin of error of the point estimate is of 6.19 minutes.

Question c:

College students tend to watch sports between 0 and 120 minutes per day, which means that the standard deviation for population can be estimated as the standard deviation of an uniform distribution with [tex]a = 0, b = 120[/tex]. This standard deviation is:

[tex]\sigma = \sqrt{\frac{(b-a)^2}{12}}[/tex]

Then

[tex]\sigma = \sqrt{\frac{(120-0)^2}{12}}[/tex]

[tex]\sigma = 34.64[/tex]

Minimum sample size:

Now, since we have an estimate for the standard deviation of the population, we use the z-distribution.

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

The minimum sample size is n for which M = 4. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]4 = 1.96\frac{34.64}{\sqrt{n}}[/tex]

[tex]4\sqrt{n} = 1.96*34.64[/tex]

[tex]\sqrt{n} = \frac{1.96*34.64}{4}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*34.64}{4})^2[/tex]

[tex]n = 288.1[/tex]

Rounding up:

The minimum sample size needed to obtain this amount of precision is 289.


Related Questions

PLEASE ANSWER ASAP WILL MARK BRAINLIEST!!

There are 5 red marbles, 15 blue marbles, and 5 green marbles in a bag. You reach in and randomly draw a marble,
replace it, and draw another marble. What is the probability that the first will be red and the second will be blue?

a.) 20%
b.) 80%
c.) 8%
d.) 12%

Answers

Answer: Hope This Helps!

Step-by-step explanation:

I would estimate around 8% or 12% is the answer. Red Marbles are a small percentage and the chance it will be picked instead of something else is rare however blue marbles are the most common and chance one will be picked is fairly high.

rotate the object 90 degrees around the origin. What are the new coordinates?

Answers

Answer:

s

Step-by-step explanation:

d

Can you please help me

Answers

Answer:

is there amultipe choice answer if so list them down

Step-by-step explanation:

What is the area of the sector for the following circle? Round your answer to 4 decimal places. *

Answers

Answer:

Area = 13.0900 ft²

Step-by-step explanation:

Area of sector = θ/360 × πr²

We are assuming it's the area of the minor sector that we are asked to find.

Therefore,

θ = 360 - 300 = 60°

r = 5 ft

Plug in the values

Area of minor sector = 60/360 × π × 5²

Area = 13.0899694

Area = 13.0900 ft² (to 4 decimal places)

Step-by-step explanation:

The angle of the minor sector will be ,

> 360 - 300 = 60° .

Area of sector :-

> Area = ∅ / 360 × πr²

> A = 60/360 × 3.14 × 5ft²

> A = 13.09 ft²

When oil is spilled in water, it creates a thin film of water approximately 1 micron thick. A barrel of oil is approximately 42 gallons of oil. If we spill a barrel of oil on the water, what is the area covered by the oil slick

Draw a sketch showing the relevant dimensions.
State your answer in square meters.
State your answer in square kilometers.

Answers

9514 1404 393

Answer:

158,987 m²0.158986 km²

Step-by-step explanation:

42 gallons is about 0.158987 cubic meters. 1 micron is 1 micro-meter, or 10^-6 meters. The volume is the product of the area and thickness. For some area A, we have ...

  0.158987 m³ = (10^-6 m)A

  A = (10^6)(0.158987 m² = 158,987 m²

The area in square meters is 158,987.

__

A square km is (1000 m)² = 10^6 m². So, the area in square kilometers is about ...

  (158,987 m²)/(10^6 m²/km²) = 0.158987 km²

The area in square km is about 0.1590.

(3^6/7^-3)= Please I need help!!!

Answers

Answer: [tex]\frac{243}{7}[/tex]

Steps:

[tex]\frac{3^6}{7^-\cdot \:3}[/tex]

[tex]\mathrm{Cancel\:the\:common\:factor:}\:3[/tex]

[tex]=\frac{3^5}{7}[/tex]

[tex]3^5=243[/tex]

[tex]=\frac{243}{7}[/tex]

Hope This Helps!

Help meeeeeee ASAP helppppppp

Answers

Answer:

45 × 1/3 = 15

Step-by-step explanation:

15 / (1/3) = (3×15)/1 = 45

so, from 15 / (1/3) = 45

we can then adapt the equation by multiplying both sides by 1/3

15 = 45 × (1/3)

Find the value of x. NO LINKS!!!​

Answers

9514 1404 393

Answer:

  z° = 44°

Step-by-step explanation:

The sum of angles in a triangle is 180°.

  44° +52° +z° +40° = 180°

  z° = 44° . . . . . . . . . . . . . . . . subtract 136° from both sides

The value of z is 44.

_____

There is no "x".

Now we have to,

→ find the required value of z.

The equation is,

→ A + B + C = 180°

Let's solve for the value of z,

→ A + B + C = 180°

→ (52 + z) + 44 + 40 = 180

→ 136 + z = 180

→ z = 180 - 136

→ [ z = 44° ]

Hence, the value of z is 44°.

Help!! If anyone could help, I’ll give Brainly! :) thank you so much

Answers

9514 1404 393

Answer:

  $50

Step-by-step explanation:

The compounding period is 1 year, and the period of concern is 1 year. This means the simple interest formula will tell the answer to the question.

  I = Prt

  I = ($5000)(0.01)(1) . . . . . r = annual rate; t = years

  I = $50

The interest earned in the account is $50.

Reese used a $60 Amazon gift card to buy stickers for her friends. After paying for 12 stickers, her balance on the gift card was $18. What was the price of each sticker, assuming all the stickers cost the same amount?

Answers

Answer:

3.5 dollars per sticker

Step-by-step explanation:

60 - 18 = 42

42 ÷ 12 = 3.5

I think this is the correct but it may be not , sorry if I wasn't that helpful...

Javier is buying oak flooring for the living room. How many square feet of flooring does he need to buy?
18 ft
9 ft
BRO
A 162 ft2
B 54 ft2
C 27 ft2
O D. 1812
PLEASE HELP ILL MARK YOU AS BRAINLESS

Answers

54 ft.

Step-by-step explanation:

add 18 on both sides which is 36. then do that with 9 9+9=18 and 18+18=36 36+18=54.

to bake a cake, the recipe calls for 6 eggs. Arline wants to bake 24 cakes for her schools bake sale. how many eggs will she need in all for the 24 cakes?

Answers

The answer is 144.

Answer:

144 eggs

Step-by-step explanation:

1 cake = 6 eggs

24 * 6 = 144 eggs in total.

A longer way to do it is by adding 6, 24 times.

6+6+6+6+6+6+6+6+6+6+6+6+6+6+6+6+6+6+6+6+6+6+6+6 = 144

But by multiplying, it makes it easier to find the answer.

What is the volume of the box

Answers

Answer:

Volume = 144 in.³

Step-by-step explanation:

Given:

Length = 9 in.

Width = 4 in.

Height = 4 in.

Required:

Volume

Solution:

Volume of a box = length * height * width

Volume = 9*4*4

= 144 in.³

4 (x + 2.5) = 48
Explain your reasoning as well.

Answers

Answer:  9.5 is the answer. You have to distribute through.

Explain: 4x+10=48

Subtract 10 from both sides you get 4x=38. Then divide both sides by 4 you get 9.5.

I need help asap:
Seventh-grade students at two different schools took the same math test at the end of the school year. Their results are shown below.



The school counselors are planning the numbers of different math classes for these students when they enter eighth grade. Which statement best describes the plan they should follow, based on the information shown?
A


School 1 should have a greater variety of math classes, since the interquartile range is much smaller than at school 2.

B


School 2 should have a greater variety of math classes, since the median is higher than at school 1.

C


School 2 should have a greater variety of math classes, since the interquartile range is much greater than at school 1.

D


School 1 should have a greater variety of math classes, since the median is lower than at school 2

Answers

i think it’s b!




sorry if i’m wrong

Answer:

its C

Step-by-step explanation:

School 1 IQR = 10

School 2 IQR = 20

Both have a median of 80

School 2

First Quartile:

70

Third Quartile:

90

School 1

First Quartile:

75

Third Quartile:

85

Please Brainiest!

Need help fast.
A pool is shaped like a rectangle with a length of 4 times its width w. What is an
expression for the distance between opposite corners of the pool?
No links or files!!!

Answers

w represents width

4w represents length

d represents diagonal

w2 + (4w)2 = d2

w2 + 16w2 = d2

17w2 = d2

±w√17 = d

 

The diagonal is the width times √17.

What is the lateral surface area, in square inches, of the figure formed by the net?

Answers

Answer:

71 in²

Step-by-step explanation:

surface area = (4×6)+(2×½×4×5)+(2×½×6×4.5)

= 24+20+27 = 71 in²

PLZZ HELP!!!
Which graph shows the solution to the system of equations 2x + y = 4 and 3x - 2y = 6?

Answers

Answer:

the last one

Step-by-step explanation:

__________________

The product n and sum of n and 76

Answers

Answer:

n+76

n --> a number not determined (and a random product)

76 --> the number the problem gave

+ --> required for addition, which provides the sum

Please answer number 9 I’ll give brainliest

Answers

Answer:

2/3 or 66.7%

Step-by-step explanation:

there are 6 possible options. 2 of them are red. 6 options minus 2 = 4=4/3=2/3

20. Miguel started with $50
in his bank account. He
deposited $20. The next day
he withdrew $40. How much
is in his bank account?

Answers

Answer:

-$10

Step-by-step explanation:

50-20=

30

30-40

= -10

50+ 20
= $70
Then subtract the $40 from the new total
70-40
=$30

What is the volume of the rectangular prism? Help pls

Answers

Answer:

10ft³

Step-by-step explanation:

3 x 5 x 2 = 30

30 x 1/3 = 10ft³

6 times the difference between q and 1

Answers

Answer:

6q-1. It's not factorsble with rational mumbers.

Answer:

6q - 6

Step-by-step explanation:

6 x (q - 1) =

6 x q - 6 x 1 =

6q - 6

Hope that helps! :)

-Aphrodite

99 is decreased to 44

Answers

Answer:

99 -? = 44.

99 -a = 44.

99 -44 -a = 44-44.

55 = a.

The interest for a bank account is compounded quarterly. The equation 480(1.08)12 is used to calculate the value of the account after some amount of time.
The yearly interest rate for the account is
8%
3%
2%
32%
12%

Answers

Answer:

8%

Step-by-step explanation:

1.08 is an increase of 0.08, which is 8%

Answer: 3%

Step-by-step explanation:

since the total amount ended up being 12 your going to divide by 4 which is the quartly amount which is how u end up with 3%.

what expressions are equivalent to 1/5•1/5•1/5•1/5

Answers

Answer:

Step-by-step explanation: Because equivalent expressions is when you Combine any like terms on each side of the equation: x-terms with x-terms and constants with constants. Arrange the terms in the same order, usually x-term before constants. If all of the terms in the two expressions are identical, then the two expressions are equivalent.

c because if you put them both in the calculator they are the same

PLEASE HELP Amber has 7 books to read. She will read 1/2 of a book each day. How many days will it take Amber to read all 7 books?

Answers

Answer:

14 days

Step-by-step explanation:

amiaoaodkwjwisodkwbqhshjdkekansxbudid

Help me HOW which choice is it

Answers

number 3 is correct

Step-by-step explanation:

smaller<bigger

Number 3 should be correct

The radius of a circle is 7 cm. Enter the circumference of the circle, in cm. Round your answer to the nearest hundredth.

Answers

Answer:

C = 43.98cm. This answer was taken online

Answer:43.98

Step-by-step explanation: Circumfernce = 2 pi r.So what we have to so is first 7(2) = 14 Next we multiply 14 by pi which is about 43.98229... Now we have to round to the nearest hundredth which is two place after the decimal point. So 8 is the number we are rounding. If we look to the right of 8 the number is 2. Anything below 5 we keep the number the same. There you have it your answer will be 43.98

what is the volume of a bow with a width of 3/2 inches a length of 5/2 inches and a height of 4 inches

Answers

Answer:

v=LxWxH

v= 3/2x5/3x4

v=15/6x4

v=10in³

Other Questions
The perimeter of a square garden is 54 feet. What is the length of one side of the garden? Reading Literature: from "The King of Mazy May," Jack London Which sentence best states the theme of the excerpt? Which monomials are perfect squares? Select THREE options:A: [tex]6x^2[/tex]B: [tex]9x^8[/tex]C: [tex]16x^9[/tex]D: [tex]25x^1^2[/tex]E: [tex]36x^1^6[/tex] The curriculum director in a large 3 points school district wants to determine the difference between the proportion of high school juniors who are enrolled in AP classes and the proportion of high school seniors who are enrolled in AP classes. She randomly selects 75 seniors and 70 juniors. Twenty-six of the seniors are enrolled in AP classes and 15 of the juniors are enrolled in AP classes. A 90 percent confidence interval for the difference between the proportion of seniors and juniors who are enrolled in AP classes is calculated. Which statement is not true? A) The critical value used is 1.645. B) The standard error of the difference is 0.074 C) The 90% interval was constructed using a method that results in intervals which capture the true difference in the proportion of seniors who are enrolled in AP classes and the proportion of juniors who are enrolled in AP classes 90% of the time. D) She can be 90% confident that the true difference between the proportion of seniors who are enrolled in AP classes and the proportion of juniors who are enrolled in AP classes is between 0.0112 and 0.2535 students. E) There is a 90% chance that the true difference between the proportion of seniors who are enrolled in AP classes and the proportion of juniors who are enrolled in AP classes is between 0.0112 and 0.2535 6)C. 1300 C.E.This map representsA)the Muslim Empires.HighlightTimeRemaining00:47:16Hide ToolsB)the Mongol Khanates.0the extent of the Ming Dynasty.D)the empire of Alexander the Great. Solve for x.x = [?]4x - 162x + 16, Somebody please help this is due in 30 minutes! (picture is attached) Anyone know this question 3. What is the author's main purpose in the article?A. to expose to people how social media only promotes certain postB. to discourage teens from posting and liking pictures on social meC. to show people why they should be mindful of what they post arD. to prove how social media is harmful to a person's mental andhealth How do I graph these points on a graph? (-1/2, -3/2) Thornton Industries began construction of a warehouse on July 1, 2021. The project was completed on March 31, 2022. No new loans were required to fund construction. Thornton does have the following two interest-bearing liabilities that were outstanding throughout the construction period:$3,000,000, 12% note$7,000,000, 7% bondsConstruction expenditures incurred were as follows:July 1, 2021 $ 700,000 September 30, 2021 990,000 November 30, 2021 990,000 January 30, 2022 930,000 The companys fiscal year-end is December 31.Required:Calculate the amount of interest capitalized for 2021 and 2022.Calculate the amount of interest capitalized for 2021. (Do not round the intermediate calculations. Round your percentage answers to 1 decimal place (i.e. 0.123 should be entered as 12.3%).)Date Expenditure Weight AverageJuly 1, 2021 x = September 30, 2021 x = November 30, 2021 x = Accumulated expenditures Amount Interest Rate Capitalized InterestAverage accumulated expenditures x % x = 2021Date Expenditure Weight AverageJanuary 1, 2022 x = January 30, 2022 x = Amount Interest Rate Capitalized InterestAverage accumulated expenditures x x = Smiling is infectiousYou catch it like the fluWhen someone smiled at me todayI started smiling tooI walked around the cornerAnd someone saw me grinWhen he smiled I realisedI had passed it on to himI thought about the smileAnd then realised its worthA single smile like mineCould travel round the earthSo if you feel a smile beginDon't leave it undetectedStart an epidemicAnd get the world infected.Can anyone plsss write a summary for the above poem plsss? 30 points for right answer +brainliest plz plz plz helpp!due in 10 mins where i live plz help!!!!!!!!!!!!!!!!!!hurryy What are some of the main character traits of Holden Caulfield in The Catcher in the Rye? A pizzeria sells a round pizza with a diameter of 16 inches. Another pizzeria sells a large square pizza with a side length of 15 inches Which of the two shapes gives you more pizza? How much more? Rounded to the nearest hundredth. Muscle tissue that is attached to what is skeletal muscle 5 bricklayers can lay a total of 50 bricks in 30 minutes. How many bricklayers willbe required to lay a total of 60 bricks in 18 minutes? How have technological improvements changed how people use digital technology? A qu se refiere la frase "El ciudadano es el eslabn clave en esta cadena de la sostenibilidad "? A. La viabilidad de una ciudad depende de sus habitantes B. Los habitantes de una ciudad deben trabajar de manera independiente C. Es importante enfatizar la eficacia de la administracin pblica D. Es clave que las personas entiendan el concepto de equilibrio natural help asap, i will give brainliest if you get it correct.