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
natulia [17]
3 years ago
12

1) Lithium isotope rations are important to medicine, the 6Li/7Li ratio in a standard reference material was measured several ti

mes, and the values are: 0.082601, 0.082621, 0.082589, 0.082617, 0.082598. Please use student’s t to find the confidence interval at the 95% confidence level. 2) If one wants the confidence interval to be two thirds of the previous one, how many times should a student repeat? (Assuming the standard deviation is the same as the previous one)?
Mathematics
1 answer:
uysha [10]3 years ago
3 0

Answer:

1) 0.0826052-2.776\frac{0.000013424}{\sqrt{5}}=0.082588    

0.0826052+2.776\frac{0.000013424}{\sqrt{5}}=0.0826219    

b) ME= 2.776\frac{0.000013424}{\sqrt{5}}=0.0000166653

And we want 2/3 of the margin of error so then would be: 2/3 ME = 0.00001111

The margin of error is given by this formula:

ME=z_{\alpha/2}\frac{s}{\sqrt{n}}    (1)

And on this case we have that ME =0.00001111016 and we are interested in order to find the value of n, if we solve n from equation (1) we got:

n=(\frac{z_{\alpha/2} s}{ME})^2   (2)

Replacing we got:

n=(\frac{2.776(0.000013424)}{0.00001111})^2 =11.25 \approx 12

So the answer for this case would be n=12 rounded up to the nearest integer

Step-by-step explanation:

Information given

0.082601, 0.082621, 0.082589, 0.082617, 0.082598

We can calculate the sample mean and deviation with the following formulas:

\bar X= \frac{\sum_{i=1}^n X_i}{n}

s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}

\bar X=0.0826052 represent the sample mean

\mu population mean

s=0.000013424 represent the sample standard deviation

n=5 represent the sample size  

Part 1

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

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

The degrees of freedom, given by:

df=n-1=5-1=4

The Confidence level is 0.95 or 95%, and the significance would be \alpha=0.05 and \alpha/2 =0.025, the critical value would be using the t distribution with 4 degrees of freedom: t_{\alpha/2}=2.776

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

0.0826052-2.776\frac{0.000013424}{\sqrt{5}}=0.082588    

0.0826052+2.776\frac{0.000013424}{\sqrt{5}}=0.0826219    

Part 2

The original margin of error is given by:

ME= 2.776\frac{0.000013424}{\sqrt{5}}=0.0000166653

And we want 2/3 of the margin of error so then would be: 2/3 ME = 0.00001111

The margin of error is given by this formula:

ME=z_{\alpha/2}\frac{s}{\sqrt{n}}    (1)

And on this case we have that ME =0.00001111016 and we are interested in order to find the value of n, if we solve n from equation (1) we got:

n=(\frac{z_{\alpha/2} s}{ME})^2   (2)

Replacing we got:

n=(\frac{2.776(0.000013424)}{0.00001111})^2 =11.25 \approx 12

So the answer for this case would be n=12 rounded up to the nearest integer

You might be interested in
Please do this correct if inappropriate then report and no LINKS and also will do brainly
Nuetrik [128]
Mean=87.5
Median=88
Mode=79,85,86,90,92,93 so technically all the numbers show are the mode cause they all repeat 1 time but if there were two of the same number that would be the mode cause there’s two and not one so you always go by which one repeats more!
4 0
2 years ago
Billy has $3.00. Bubble gum costs $.30. He bought four pieces.
xenn [34]

Answer:

$0.30 x 4= $1.20

$3.00 divided by $1.20= $1.80

Step-by-step explanation:

I hope this is what you were looking for

7 0
3 years ago
Read 2 more answers
3. The cost of a ticket twill be no more than $26.
goblinko [34]
Any number 1-26 should work. the expression would me x<$26.
7 0
3 years ago
Please help! I’ll give brainliest
Vilka [71]

Answer:

Step 1: Simplify both sides of the equation.

−7f=12

Step 2: Divide both sides by -7.

−7f

−7

=

12

−7

f=

−12

7

Step-by-step explanation

sorry for the answer like this i couldnt find the fractions but the answer is f=-12/7 sorry :(

6 0
2 years ago
7/2x + 1/2x = 7 + 9/2x
lesya [120]

Answer: x=-14

Step-by-step explanation:

5 0
1 year ago
Other questions:
  • The classroom has 4 desks in each row. There are 5 rows. How many desks are there in the classroom?
    8·2 answers
  • If a triangular prism has a height of 9 a width of 9 and length of 6 what is the volume in cm3
    10·1 answer
  • Estimate 726 Times 5
    6·1 answer
  • Which of the numbers below is greatest? <br><br> -2, -2.3, -2.5, -2 2/3
    6·2 answers
  • Question number 7 Give a reasonable domain and range for the function in this context
    5·1 answer
  • Find the value of x (4x-10)/(x)
    11·1 answer
  • What does |-7|+5 equal too?
    13·2 answers
  • When the base of the ladder is 10 ft away from the base of a building, the top of the ladder touches the building 18 ft above th
    8·1 answer
  • Consider the angle 0.<br> What is the value of the ratio opposite/adjacent
    7·1 answer
  • A group of 5 friends went out to dinner. The total bill including the tax and tip came to $83.95. If they split the bill evenly,
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!