1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
joja [24]
3 years ago
12

We draw a random sample of size 36 from a population with standard deviation 3.5. If the sample mean is 27, what is a 95% confid

ence interval for the population mean?
Mathematics
2 answers:
inessss [21]3 years ago
3 0

Answer:

The 95% confidence interval for the population mean is between 25.86 and 28.14.

Step-by-step explanation:

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

\alpha = \frac{1-0.95}{2} = 0.025

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

So it is z with a pvalue of 1-0.025 = 0.975, so z = 1.96

Now, find the margin of error M as such

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

M = 1.96\frac{3.5}{\sqrt{36}} = 1.14

The lower end of the interval is the sample mean subtracted by M. So it is 27 - 1.14 = 25.86

The upper end of the interval is the sample mean added to M. So it is 27 + 1.14 = 28.14

The 95% confidence interval for the population mean is between 25.86 and 28.14.

yaroslaw [1]3 years ago
3 0

Answer:

27-1.96\frac{3.5}{\sqrt{36}}=25.857  

27+1.96\frac{3.5}{\sqrt{36}}=28.143  

The 95% confidence interval would be given by (25.857;28.143). And we can conclude that the true mean with 95% is between (25.857;28.143)

Step-by-step explanation:

Data given

\bar X=27 represent the sample mean  

\mu population mean (variable of interest)  

\sigma=3.5 represent the population standard deviation  

n=36 represent the sample size  

95% confidence interval  

The confidence interval for the mean is given by the following formula:  

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}} (1)  

Since the Confidence is 0.95 or 96%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that z_{\alpha/2}=1.96  

Now we have everything in order to replace into formula (1):  

27-1.96\frac{3.5}{\sqrt{36}}=25.857  

27+1.96\frac{3.5}{\sqrt{36}}=28.143  

The 95% confidence interval would be given by (25.857;28.143). And we can conclude that the true mean with 95% is between (25.857;28.143)

You might be interested in
Math help owo pls will reword #_# pleath
timama [110]

Question 13: The answer is D

Question 7: The answer is C

Question 14: The answer is B

And the question for the last Pic, the correct graph is B.

8 0
3 years ago
Read 2 more answers
An equation is shown below:
mart [117]
Multiple 6 with numbers inside paranthesis:
12x - 66 + 15 = 21
add 66 fhen substrack 15 from both sides :
12x = 72 divide both sides with 12:
x = 6

5 0
3 years ago
Read 2 more answers
Expanded form for 13 cubed
saw5 [17]
The answer to this question is 2197! Hope this helped :3
5 0
3 years ago
What are the common factors common factors of 60,36 and 48?
nikitadnepr [17]
The answer is 2×2×3

if needed to be multiplied together the answer is 12
5 0
3 years ago
(HELP) The point (- 8, - 2) is on the parent graph below. Where will it be on the transformed graph?
olga2289 [7]

Answer:

   x=\frac{y2 }{9}

Step-by-step explanation:

2nd step: 3\sqrt{x}=y

third step: \frac{3\sqrt{x} }{3} = \frac{y}{3}

fourth step: \sqrt{x} =\frac{y}{3}

answer:    x=\frac{y2 }{9}

4 0
3 years ago
Other questions:
  • A fossilized leaf contains 8% of its normal amount of carbon 14. How old is the fossil (to the nearest year)? Use 5600 years as
    14·1 answer
  • How do you solve this?
    13·1 answer
  • Georgia is 2 years younger than 1/3 of her Aunt Mika's age. Write an expression that describes Georgia's age. How old is Georgia
    13·1 answer
  • Which system of inequalities is represented by the graph?<br> A) A <br> B) B <br> C) C <br> D) D
    8·1 answer
  • Round 41.805 to the nearest whole number
    7·2 answers
  • Simplify the expression square root of 15•square17
    7·1 answer
  • I need gay guy friends or maybe even more then friends in the future
    13·1 answer
  • What is 6 divided by 0.6
    7·1 answer
  • Please help me now! (For the first and the second.)
    13·2 answers
  • What would be the second step in this problem? (3 + 4) 9 + 3 =
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!