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

Guys I need some help

Answers

The answer is c your welcome

Write the ratio as a fraction in lowest term: 15 to 36​

Answers

Answer:

5/12

Step-by-step explanation:

15 to 36 can also be written as 15/36.

Divide by common values to simplify.

15÷3/36÷3

5/12

Best of Luck!

What is 1/32 as a decimal

Answers

Answer:

0.03125

Hope this helps! :)

0.03125 is the answer :) hope it helped

What expression is equivalent to 12y + (7y)(3)

Answers

Answer:

I got 33y

Step-by-step explanation:

hi if its right but here

Answer:

57y

Step-by-step explanation:

Let tk be the number of ways to choose k beads from a drawer that contains 10 red beads, 8 blue beads, and 11 green beads. Find the generating function for the sequence {tk} 29 k = 0. Do not find a formula for tk.

Answers

Answer:

[tex]\mathbf{G(x) = (1 + x)^{29}}[/tex]

Step-by-step explanation:

From the given information;

The total number of beads  = 10 + 8 + 11 = 29

To choose k beads out 29 beads, let assume that [tex]t_k[/tex] be the no. such that:

[tex]t_k = ( ^{29}_{k}) \ \ \ where; k =0,1,2,3,....,29[/tex]

The sequence [tex]\{ t_k\}^{29}_{k=0} = (^{29}_{k})[/tex]

The generating function for [tex]\{ a_k \}^n_{k=0}[/tex] is:

[tex]G(x) = a_o +a_1x +a_2x^2 +...+a_nx^n[/tex]

[tex]G(x) = \sum \limits ^{n}_{k=0} \ a_k x^k[/tex]

For the sequence above;

[tex]G(x) = \sum \limits ^{29}_{k =0 } (^{29}_{k}) x^k[/tex]

By applying binomial series [tex](1+x)^n = \sum \limits ^n_{k=0} ( ^n_k) x^k[/tex]

Thus:

[tex]\mathbf{G(x) = (1 + x)^{29}}[/tex]

Black friday sale on TVs were 50 in tv for $148.00 or 65 in for $199.00 which is the better buy this is not worth a grade just some understanding​

Answers

Answer:

i personally think the 65 in. one

Step-by-step explanation:

A and B are independent events.
P(A) = 0.6
P(B) = 0.4
What is P(AB)?
O A. 0.24
O B. 0.6
O C. 0.4
D. Not enough information

Answers

Answer:

Not enough information

In a recent year, 6% of cars sold had a manual transmission. A random sample of college students who owned cars revealed the following: out of 124 cars, 29 had manual transmissions. Estimate the proportion of college students who drive cars with manual transmissions with 90% confidence.

Answers

Answer:

The  estimate the proportion of college students who drive cars with manual transmissions with 90% confidence is  

      [tex]0.171 <  p <  0.297 [/tex]  

Step-by-step explanation:

From the question we are told that

    The sample size is  n  =  124

    The population proportion p =  0.06

     The number of cars with manual transmissions is  k =  29

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]

Generally the sample proportion is mathematically represented as

       [tex]\^ p = \frac{ 29 }{124 }[/tex]

=>   [tex]\^ p = 0.234[/tex]

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

   [tex]Z_{\frac{\alpha }{2} } =  1.645 [/tex]  

Generally the margin of error is mathematically represented as  

     [tex]E =  Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} } [/tex]

=>   [tex]E =   1.645  * \sqrt{\frac{0.234 (1- 0.234 )}{124} } [/tex]

=>   [tex]E =  0.063  [/tex]

Generally 95% confidence interval is mathematically represented as  

      [tex]\^ p -E <  p <  \^ p +E[/tex]

=>  [tex]0.234  - 0.063  <  p <  0.234  + 0.063 [/tex]

=>  [tex]0.171 <  p <  0.297 [/tex]  

Choose the equation that represents the asymptote of the graph f(x) = 2^x +3.

y = 0
y = 3
x = 0
x = 3​

Answers

Answer:

x = 0

Step-by-step explanation:

The horizontal asymptote occurs at x = 0, Hence the equation that represents the asymptote of the graph is at x = 0

f(x) = 2^x +3.

0 = 2^x +3.

2^x +3. = 0

2^x = -3

log 2^ x = log(-3)

x log2 = log(-3)

x = log(-3)/log 2

Hence the required function is when x = 0

Find the unit rate. Round to the nearest hundredth, if necessary.

$5.99 for 18 lb

The unit rate is ?/b

Answers

the answer for this is 3.0

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D. $700

Answers

The answer to this question is D

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Answers

C is the answer
(-3)^2=9
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C. Add 6 and 10.
D. Evaluate 8².​

Answers

Answer:

D

Step-by-step explanation:

Solve for x in each of the following diagrams. ​

Answers

In the left one x equals 12.9 and on the right one x equals 11

A glider flies 8 miles south from the airport and then 15miles east. Then it flies in a straight line back to. What was the distance of the glider’s last trip back to the airport?

Answers

17 miles
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Solve x^2 + 6x + 15 = 0 using the Quadratic Formula

Answers

I hope the following helps!!

i am a decimal number less than 1. the digit in my tenths place is an even prime number. my hundredths digit is twice my tenths digit, and my hundred thousandths digit is twice my hundredths digit. the thousandths digit is three less than my hundredths digit. my ten thousandths digit is the sum of my tenths and thousandths digit. what number am i?

Answers

Answer:

.

Step-by-step explanation:

Answer:

0.24857

Step-by-step explanation:

Less than 1 is 0. and

only even prime is 2

Can someone help me on these questions?

Answers

Me not good on math matics I sorry hybrid

Answer:

I can give you a few of them, sorry

Step-by-step explanation:

5) obtuse 6)straight 7)right 9) 24°

I WILL GIVE BRAINLIEST TO WHOMEVER ANSWERS FIRST

Answers

This is VERY VERY simple! Find the rule. Multiply the individual cost by x. You should be able to find the answer from there... for the last row, multiply your individual cost by 13.

Are the equation linear or nonlinear?​

Answers

Answer:

Results below

Step-by-step explanation:

Equation of the line

A straight line can be written in the form:

y = ax + b

Where a and b are constants and x is the independent variable.

The essential condition for an equation to be linear is that the x must be powered to the exponent 1, which is usually not written.

From the equations presented in the table:

[tex]y = x^1+2[/tex] is linear because the exponent of the x is 1

y = 5(x+2) = 5x + 10 is linear with a=5 and b=10.

y = x is linear with a=1 and b=0

[tex]y = x^2+1[/tex] is not linear because the exponent of x is 2

[tex]y = x(x) = x^2[/tex] is not linear because the exponent of x is 2

The table below summarizes the results


By the Exterior Angle Theorem, which of the following is a true statement?

Answers

Answer:

2nd option is the correct answer

Step-by-step explanation:

[tex]m \angle 1 > m \angle 3 \: \& \: m \angle 1 > m \angle 7 \\ [/tex]

According to the Exterior Angle Theorem, the true statement should be considered as the option b.

What is an Exterior Angle Theorem?

The exterior angle theorem defined that at the time when a triangle's side should be extended, the resultant exterior angle formed should be equivalent to the sum of the measures of the two opposite interior angles of the triangle.

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learn more about an angle here: https://brainly.com/question/6150811

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Answer:

me depending on what kind of math it is

Step-by-step explanation:

Please explain how to do this please show work

Answers

Answer:

(x-1)(x+4)

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Xsquare +4x -x -4

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Answer:

what are you trying to ask?

Step-by-step explanation:

7 filler filler filler

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Answers

The space from -3 to 0 is 3 units. The answer is positive 3, not negative.

HELP ME PLEASEEEE :)

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Answer:

I believe it to be C

Step-by-step explanation:

How many ways are there to rearrange the letters ALIVE in such a way that the word EVIL is not contained in the resulting word

Answers

Answer: 118 combinations.

Step-by-step explanation:

In ALIVE we have 5 letters, rearranging it we have the possible options of:

5 options for the first letter.

4 options for the second letter, as one was already chosen for the first one

3 options for the third letter, as 2 were already chosen.

2 options for the fourth letter.

1 option for the last letter.

The total number of combinations will be equal to the product of the numbers of options for each letter, then we have:

5*4*3*2*1 = 120 combinations.

And the combinations where the word EVIL is formed are:

AEVIL

EVILA

2 combinations, then the total number of combinations such that the word evil is not formed are:

120 - 2 = 118 combinations.

Which of the following are two-step equations? Choose more than
one answers

Answers

Answer:

i think a b d f

Step-by-step explanation:

Elvira makes money to buy decorations for the cafeteria by selling little bags of chips in the snack bar. If each bag costs $0.35 and she can sell the bag for $0.90, how many bags must she sell to earn at least $200.

Answers

Answer:

Step-by-step explanation:

.90-.35=.55

200/.55=364 bags i think

Elvira sells a total of 364 bags to earn a profit of $200 and this can be determined by using the unitary methods.

Given :

Elvira makes money to buy decorations for the cafeteria by selling little bags of chips in the snack bar. If each bag costs $0.35 and she can sell the bag for $0.90.Total profit earn = $200

The following steps can be used to determine the total number of bags she sells to earn the profit of $200:

Step 1 - First find the total profit she earns to sell one bag.

= 0.90 - 0.35

= $0.55

Step 2 - Now, using the unitary method find the total number of bags she sells to earn a profit of $200 If she earns a profit of $0.55 to sell one bag.

[tex]=\dfrac{200}{0.55}[/tex]

= 363.63 [tex]\approx[/tex] 364 bags

She sells a total of 364 bags to earn a profit of $200.

For more information, refer to the link given below:

https://brainly.com/question/23423168

2. Sandra plans to swim a total of 2 2/3 miles every week for 2 1/5
weeks. How many miles is Sandra planning on swimming?

Answers

Answer:

5 13/15 miles

Step-by-step explanation:

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