Based on a sample of 100 employees a 95% confidence interval is calculated for the mean age of all employees at a large firm. The interval is (34.5 years, 47.2 years).
A. What was the sample mean?
B. Find the margin of error?
C. Find the critical value tc for:
a. a 90% confidence level when the sample size is 22.
b. an 80% confidence level when the sample size is 49.

Answers

Answer 1

Answer:

a

[tex]\= x = 40.85[/tex]

b

[tex]E = 5.85[/tex]

Ca  

   [tex]t_c =  2.08 [/tex]

Cb

   [tex] t_c  =   1.282 [/tex]

Explanation:

From the question we are told that

     The sample size is n  =  100

     The upper limit of the 95% confidence interval is  b =  47.2 years

     The lower limit of the 95% confidence interval is   a =  34.5 years

Generally the sample mean is mathematically represented as

         [tex]\= x = \frac{a + b }{2}[/tex]

=>    [tex]\= x = \frac{47.2 + 34.5 }{2}[/tex]

=>    [tex]\= x = 40.85[/tex]

Generally the margin of error is mathematically represented as

         [tex]E = \frac{b- a }{ 2}[/tex]

=>      [tex]E = \frac{47.2- 34.5 }{ 2}[/tex]

=>      [tex]E = 5.85[/tex]

Considering question C a  

From the question we are told the confidence level is  90% , hence the level of significance is    

      [tex]\alpha = (100 - 90 ) \%[/tex]

=>   [tex]\alpha = 0.10[/tex]

The  sample size is  n =  22

Given that the sample size is not sufficient enough i.e [tex]n < 30[/tex] we will make use of the student t distribution table  

Generally the degree of freedom is mathematically represented as

           [tex]df = n- 1[/tex]

=>        [tex]df = 22 - 1[/tex]

=>        [tex]df = 21[/tex]

Generally from the student  t  distribution table the critical value  of  [tex]\frac{\alpha }{2}[/tex] at a degree of freedom  of  21 is  

   [tex]t_c =t_{\frac{\alpha }{2} ,  21  } =  2.08 [/tex]

Considering question C b

From the question we are told the confidence level is  80% , hence the level of significance is    

      [tex]\alpha = (100 - 80 ) \%[/tex]

=>   [tex]\alpha = 0.20[/tex]

Generally from the normal distribution table the critical value  of  [tex]\frac{\alpha }{2}[/tex] is  

   [tex] t_c  =Z_{\frac{\alpha }{2} } =  1.282 [/tex]


Related Questions

what is 30 percent of 64?

Answers

Answer:

19.2

Step-by-step explanation:

I did the math by dividing the percentage and total

What is the missing number?"
IN
OUT
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Number 6 hopefully it helped

Name the corresponding an

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Answer:

what do you want to say?

umm girll what? lol i’m so confused

PLEASE ANSWER I WILL GIVE BRAINLIEST TO WHOMEVER ANSWERS FIRST

Answers

Answer

x to 0

10 to 350

hope that helps you:)

please mark me brainiest

tryna get 3 brainiest

HELP ASAP "Steve's mom gives him 50$ to spend at the mall. He must but two new pairs of pants which each cost 19$ each. He can spend the rest at an arcade where each game cost 0.75
Which inequality can be used to determine the number (n) of arcade games Steve can play?


19 + 0.75n <50

19 + 0.75, n , <50

38 + 0.75n <50

38 + 0.75, n , <50

19 + 0.75n ≤50

19 + 0.75, n is less than or equal to, 50

38 + 0.75n ≤50

Answers

I really don’t know I’m sorry:(

Answer:

bro i'm literally doing math homework right now and i don't know ANYTHING about it. so dude i def cant help u i'm sorry :')

Step-by-step explanation:

Abel Alonzo, Director of Human Resources, is exploring employee absenteeism at the Harrison Haulers Plant. Abel knows that absenteeism varies significantly between departments. For example, workers in the wood shop are absent more than those in the tuning department and the size of the departments ranges from 40 to 120 workers. He orders a random sample of 10 workers from each of the six departments. Abel's sample is a

Answers

Answer:

disproportionate stratified sample

Step-by-step explanation:

Based on the given information we can say that Abel's sample is a disproportionate stratified sample. This is the case mainly because the department worker population ranges from 40 to 120 workers. This changing population makes the 10 workers that were chosen for the sample not proportionate to the entire population. Therefore, under different population sizes workers have different chances of getting selected for the study which ultimately creates different results.

Find the slope of a line that passes through points (-2,1) and
(3,-5)

Answers

Answer:

-1.2

Step-by-step explanation:

Answer:

-6/5=M

Step-by-step explanation:

2х + y = 4
у = 3х – 1

Answers

its 2 because 2plus is 2

please help me with this will give brainliest to best answer

Answers

Answer:

this may sound crazy but its A,B,C,D

Step-by-step explanation:

they not in the boundaries 0f 5 to 0 or -2 to 0

Which model shows two equal expressions when the value of X is 4

Answers

Answer:

A

Step-by-step explanation:

A has 4 boxes with XS and the end result is 4 1s which add up to 4 Xs

Answer:

A

Step-by-step explanation:

Fill in the blank to find the y-intercept of-x+2y=10

Answers

I think x is 20 I’m not sure tho since it would come out as -10 instead of positive

simplify the following expression 3 [(x^3-7x+1)-(x+4)]

Answers

Answer: 3x^3−24x−9

Step-by-step explanation: 3(x^3−7x+1−(x+4))

=(3)(x^3+−7x+1+−x+−4)

=(3)(x^3)+(3)(−7x)+(3)(1)+(3)(−x)+(3)(−4)

=3x^3−21x+3−3x−12

=3x^3−24x−9

PLSSSS HELP WILL MARK BRAINLIESTTT
QUESTION 15

Answers

it’s both (0,-2) and (-6,0) though

Now I need thissss pls

Answers

I think it’s 25 because 65 + 90 is 155 + 25 is 180

Student tickets cost $6.25 each at a local movie theater. Which proportion could be used to find the number of student tickets, t, that could be purchased with a $25 gift card?

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Answer:

4

Step-by-step explanation:

bc I got jt right

WILL MARK BRAINLIEST!!

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Answer:

only p(x)

Step-by-step explanation:

The others have a restricter domain

image to help also needed asap :/

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Answer:

Its c/2

Step-by-step explanation:

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Tricia has $37.25 in her account. Which shows the amount she will have left after she writes a check for $23.99?
A. $12.36
B. $12.74
C. $13.26
D. $13.74

Answers

C :) brainiest? This is correct because I did the math lol

The amount she will have left after writing a check for $23.99 is $13.26. The correct answer would be an option (C).

What is the Subtraction operation?

Subtraction is a mathematical operation that deducts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

Tricia has $37.25 in her account, if she writes a check for $23.99, to find the amount left after that we need to subtract the check amount from her initial amount.

⇒ initial amount - check amount

⇒ $37.25 - $23.99

Apply the subtraction operations, and we get

⇒ $13.26

Therefore, the amount she will have left after writing a check for $23.99 is $13.26.

Learn more about Subtraction operations here:

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Need help Pronto! Will give braintliest.

Answers

Answer:

b

Step-by-step explanation:

i’m pretty sure it’s B, but i’m not 100% sure, sorry if it’s wrong :(

I
Tori had a $300 unpaid balance after last month's payment on her account. Her annual percentage rate is 21%. The minimum payment due is $25. How much of that is interest for one
month on the unpaid balance?

Answers

Answer:

After the passage of a month, the interest that Tori must pay will be $ 4.81.

Step-by-step explanation:

Given that Tori has an unpaid balance of $ 300 on her credit card, and that said credit card has an annual interest of 21% on the unpaid balances, considering that the minimum payment is $ 25, to determine how much she should pay after a month of After your debt, it is necessary to perform the following calculation:

12 = 21

1 = X

21/12 = X

1.75 = X

((300 - 25) x 1.75 / 100) + 300 = X

4.81 + 300 = X

304.81 = X

Thus, after the passage of a month, the finance charge that Tori must pay will be $ 4.81.

The table below shows the possible outcomes of rolling a six-sided number cube and flipping a coin.

A 7-column table with 2 rows. Column 1 has entries H, T. Column 2 is labeled 1 with entries H 1, T 1. Column 3 is labeled 2 with entries H 2, T 2. Column 4 is labeled 3 with entries H 3, T 3. Column 5 is labeled 4 with entries H 4, T 4. Column 6 is labeled 5 with entries H 5, T 5. Column 7 is labeled 6 with entries H 6, T 6.

What is the probability of getting a number less than 3 and a tails?
StartFraction 1 over 12 EndFraction
StartFraction 1 over 6 EndFraction
One-fourth
One-third

Answers

Answer:

B: 1/6

Step-by-step explanation:

edg2020

Answer:

B

Step-by-step explanation:

on edge 2020-2021

5.
3x3 + 2y2 - xy for x = 2 and y = 3

Answers

Answer:

21

Step-by-step explanation:

HELP PLEASE!! Two lines are drawn in the same plane.
Under what condition are the lines
perpendicular?
A two lines that never intersect
B. two lines that intersect and form right angles
C. two lines that intersect and form acute angles
D. two lines that intersect at more than one point

Answers

Answer:it is c or b

Step-by-step explanation:

The condition for the lines to be perpendicular will be two lines that intersect and form right angles. Then the correct option is B.

What is a linear equation?

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Two lines are drawn in the same plane.

If the two lines intersect then the angle between the line is 90 degrees.

The condition for the lines to be perpendicular will be two lines that intersect and form right angles.

Then the correct option is B.

The graph is given below.

More about the linear equation link is given below.

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Find the area of a circle with diameter 12 m.
Use the value 3.14 for n, and do not round your answer.
Be sure to include the correct unit in your answer.

Answers

Answer:

113.04m²

Step-by-step explanation:

Area of circle: [tex]\pi[/tex] × r²

Radius = [tex]\frac{diameter}{2}[/tex]

We can just apply the formula to the question:

Area of circle = 3.14 × ([tex]\frac{12}{2}[/tex])²

                      = 3.14 × 36

                      = 113.04m²

Combine like terms in the expression 7a-4b+5b-a

Answers

Answer:

6a+b

Step-by-step explanation:

pls mark me brainliest

What is the length of each leg
the triangle below?

A. 5.6
B. v32
C. 16
D. 4v2
E. 16v2
F. 1

Answers

E is the answer. Since it’s a 45 45 90 triangle the rules are the hypotenuse is equal to x squareroot of 2 while the two other sides are just equal to x. If Xv2= 32 then the two sides (x) must be equal to 16v2

The length of each leg of the given triangle is 16√2.

What is the triangle?

Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.

The length of the leg is calculated by using the angle property. Use sin angle to calculate each leg.

First leg,

Sin45 = P / H

1 / √2 = P / 32

P = 32 / √2

P = 16√2

Second leg,

Sin45 = P / H

1 / √2 = P / 32

P = 32 / √2

P = 16√2

Therefore, the length of each leg of the given triangle is 16√2.

To know more about triangles follow

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Proportions 6. A certain salsa is made with 6 parts tomato and 2 parts bell pepper. How many cups of tomato should be combined with 1.5 cups bell pepper? Write a proportion, then solve. ​

Answers

Answer:

4.5 cups of tomatoes should be combined with 1.5 cups of bell peppers.

Step-by-step explanation:

Given that the salsa is made with 6 parts tomato and 2 parts bell pepper.

Let t be tomatoes and b be bell peppers

The proportion will be:

t:b

The ratio of tomatoes to bell pepper will be:

6:2

This ratio simplifies to 3:1

This means no matter how much more the tomatoes and peppers are, the simplified ratio will be same.

Now the bell peppers are 1.5 cups then the proportion will be:

[tex]t:b::t:b\\6:2::t:1.5\\\frac{6}{2} = \frac{t}{1.5}\\3 = \frac{t}{1.5}\\t = 1.5 * 3\\t =4.5[/tex]

Hence,

4.5 cups of tomatoes should be combined with 1.5 cups of bell peppers.

You want to know about the dining habits of college students in the US. Since you do not have resources to survey all college students in the nation, you take a random sample of 1501. You learn that, on average, they eat out 4 times per week. Also, these sample data are generally distributed about the average of 4 times, by 1.5 times per week. 1. What is the average times per week that college students across the nation eat out

Answers

Answer:

the average times per week that college students across the nation eat out lies within these 95% confidence interval

      [tex] 3.938  <  \mu < 4.062 [/tex]

Step-by-step explanation:

From the question we are told that

    The sample size is n =  1501

    The sample mean  is  [tex]\= x = 4[/tex]

      The standard deviation is  [tex]\sigma = 1.5[/tex]

From the question we are told the confidence level is  95% , hence the level of significance is    

      [tex]\alpha = (100 - 95 ) \%[/tex]

=>   [tex]\alpha = 0.05[/tex]

Generally from the normal distribution table the critical value  of  [tex]\frac{\alpha }{2}[/tex] is  

   [tex]Z_{\frac{\alpha }{2} } =  1.96[/tex]

Generally the margin of error is mathematically represented as  

      [tex]E = Z_{\frac{\alpha }{2} } *  \frac{\sigma }{\sqrt{n} }[/tex]

=>   [tex]E = 1.96  *  \frac{1.5 }{\sqrt{1501} }[/tex]

=>   [tex]E = 0.06196 [/tex]

Generally the estimate for average times per week that college students across the nation eat out at a 95% confidence is  mathematically represented as

      [tex]\= x -E <  \mu <  \=x  +E[/tex]

      [tex]4  -0.06196  <  \mu < 4  + 0.06196[/tex]

=>   [tex] 3.938  <  \mu < 4.062 [/tex]

Hence the true average times per week that college students across the nation eat out lies within this interval

A painter uses 1.5 gallons of paint to cover 3/4 of a wall. At this rate, how many gallons of paint does it take to paint the entire wall? ​

Answers

Answer:

[tex]6[/tex]

Step-by-step explanation:

if

[tex] \frac{3}{4} = 1.5 \\ \\ \frac{4}{4} = \frac{4}{4} \times 1.5 \times \frac{4}{3} \\ \\ = 6[/tex]

8(0.25n-2)+n=-0.5(8-4n)

Answers

The answer should be n = 12. Hope this helps.
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