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
Black_prince [1.1K]
2 years ago
6

A research engineer for a tire manufacturer is investigating tire life for a new rubber compound and has built 16 tires and test

ed them to end-of-life in a road test. The sample mean and standard deviation are 60,139.7 and 3645.94 kilometers.
Find a 95% confidence interval on mean tire life.
Mathematics
2 answers:
lesya692 [45]2 years ago
7 0

Answer:

60139.7-2.131\frac{3645.94}{\sqrt{16}}=58197.33    

60139.7+2.131\frac{3645.94}{\sqrt{16}}=62082.07    

So on this case the 95% confidence interval would be given by (58197.33;62082.07)    

Step-by-step explanation:

Previous notation

\bar X= 60139.7 represent the sample mean

\mu population mean (variable of interest)

s=3645.94 represent the sample standard deviation

n=16 represent the sample size  

Solution to the problem

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

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

In order to calculate the critical value t_{\alpha/2} we need to find first the degrees of freedom, given by:

df=n-1=16-1=15

Since the Confidence is 0.95 or 95%, 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: "=-T.INV(0.025,15)".And we see that t_{\alpha/2}=2.131

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

60139.7-2.131\frac{3645.94}{\sqrt{16}}=58197.33    

60139.7+2.131\frac{3645.94}{\sqrt{16}}=62082.07    

So on this case the 95% confidence interval would be given by (58197.33;62082.07)    

frutty [35]2 years ago
3 0

Answer:

The 95% confidence interval for mean tire life is between 52,368.4 kilometers and 67,911 kilometers.

Step-by-step explanation:

We are in posession of the sample's standard deviation, so we use the students t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 16 - 1 = 15

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 15 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975. So we have T = 2.68

The margin of error is:

M = T*s = 2.1315*3645.94 = 7771.3

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 60139.7 - 7771.3 = 52,368.4.

The upper end of the interval is the sample mean added to M. So it is 60139.7 + 7771.3 = 67,911.

The 95% confidence interval for mean tire life is between 52,368.4 kilometers and 67,911 kilometers.

You might be interested in
What system of inequalities is represented by the graph?
Juli2301 [7.4K]
One solution is the answer
6 0
2 years ago
Find the scale factor
RSB [31]

Answer:

3

Step-by-step explanation:

4*3=12

3*3=9

5*3=15

So you find the number that can be multiplied or divided by each side the same to get the new number

5 0
2 years ago
Read 2 more answers
Help me and you will get more points
AlekseyPX

z = 3m - 2n

Step-by-step explanation:

1000^m ÷ 100^n

Rewrite them in exponent form

That's

10^3m ÷ 10^2n

Since the bases are the same and they are dividing we subtract the exponents

That's

10^3m - 2n

Comparing it with 10^z

10^3m - 2n = 10^z

z = 3m - 2n

Hope this helps you

3 0
2 years ago
A worker has dug 5 holes for a fence post. It will take 20 minutes to dig each addional
anzhelika [568]

Answer:

it 100

Step-by-step explanation:

firs take the zero then time with the 5 it would give 10 n

then add the zero so 100

5 0
2 years ago
If a university wants to maintain a 14:1 ratio between students and teachers, how many teachers would be needed to accommodate 8
zheka24 [161]
<span>So we want to know the number of teachers the university should have if the ratio of students to teachers is 14:1 and the number of students is 896. If x is the number of teachers: 14/1=896/x. Now we solve for x: Lets multiply both sides with x: x*(14/1)=896 and divide both sides by 14 and we get: x=896/14 and x=64. So the university should have 64 teachers.</span>
7 0
3 years ago
Read 2 more answers
Other questions:
  • If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 ft per second, then its height h
    12·2 answers
  • Find the GCF of the numbers 45 and 76 using lists<br> of factors.
    9·1 answer
  • The equation below describes a parabola. If a is positive, which way does the parabola open?
    11·2 answers
  • What is the sum of 16.5 x 10 exponent 4
    7·2 answers
  • Is the slope of the linear positive, negative,zero, or undefined<br> y=-x+5
    6·1 answer
  • HELP PLZ I don't know how to coordinate planes
    8·1 answer
  • D over 12 when d= 36
    10·2 answers
  • What is the distance between the points (-3,5) and (-3,-9) ? ​
    15·1 answer
  • Work out the temperature
    15·1 answer
  • Find the mode of the set of numbers (6,12,9,9,6,12,3,3,12,12)
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!