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]


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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

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.

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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 :(

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

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