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
Ganezh [65]
3 years ago
12

The tensile strength of stainless steel produced by a plant has been stable for a long time with a mean of 72 kg/mm2 and a stand

ard deviation of 2.15. A machine was recently adjusted and a sample of 50 items were taken to determine if the mean tensile strength has changed. The mean of this sample is 74.28. Assume that the standard deviation did not change because of the adjustment to the machine. Find a 95% confidence interval for the mean of tensile strength after the machine was adjusted. Does this data suggest that the tensile strength was changed after the adjustment
Mathematics
1 answer:
Elanso [62]3 years ago
8 0

Answer:

95% confidence interval for the mean of tensile strength after the machine was adjusted is [73.68 kg/mm2 , 74.88 kg/mm2].

Yes, this data suggest that the tensile strength was changed after the adjustment.

Step-by-step explanation:

We are given that the tensile strength of stainless steel produced by a plant has been stable for a long time with a mean of 72 kg/mm 2 and a standard deviation of 2.15.

A machine was recently adjusted and a sample of 50 items were taken to determine if the mean tensile strength has changed. The mean of this sample is 74.28. Assume that the standard deviation did not change because of the adjustment to the machine.

Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;

                         P.Q. = \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \bar X = sample mean strength of 50 items = 74.28

            \sigma = population standard deviation = 2.15

            n = sample of items = 50

            \mu = population mean tensile strength after machine was adjusted

<em>Here for constructing 95% confidence interval we have used One-sample z test statistics as we know about population standard deviation.</em>

So, 95% confidence interval for the population mean, \mu is ;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level of

                                                  significance are -1.96 & 1.96}  

P(-1.96 < \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < 1.96) = 0.95

P( -1.96 \times {\frac{\sigma}{\sqrt{n} } } < {\bar X-\mu} < 1.96 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.95

P( \bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } } < \mu < \bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.95

<u><em>95% confidence interval for</em></u> \mu = [ \bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } } , \bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } } ]

                 = [ 74.28-1.96 \times {\frac{2.15}{\sqrt{50} } } , 74.28+1.96 \times {\frac{2.15}{\sqrt{50} } } ]

                 = [73.68 kg/mm2 , 74.88 kg/mm2]

Therefore, 95% confidence interval for the mean of tensile strength after the machine was adjusted is [73.68 kg/mm2 , 74.88 kg/mm2].

<em>Yes, this data suggest that the tensile strength was changed after the adjustment as earlier the mean tensile strength was 72 kg/mm2 and now the mean strength lies between 73.68 kg/mm2 and 74.88 kg/mm2 after adjustment.</em>

You might be interested in
Perimeter of a square with side 4 square root of 5
Darya [45]

Answer:

16\sqrt{5}

Step-by-step explanation:

4\sqrt{5}+4\sqrt{5}+4\sqrt{5}+4\sqrt{5}

16\sqrt{5}

7 0
3 years ago
ASAP please help!!!
Serggg [28]
Y+4<u><</u>9
subtract 4
y<u><</u>5
y is smaller than and equal to 5
so you shade from 5 to the negative end to infinity (to the left) and shade the 5 to show that it is included (attachment says A)







6 less than (-6) 2 times a number (2 time x) is greater than (>) 8 (8)

-6+2x>8
add 6
2x>14
divide 2
x>7
so
x is bigger than 7
shade from 7 to the positive end to infinity (to the right) and don't shade 7 but put a circle around it to show that it is not included (attachment says B )

I have included pictures of the number lines

4 0
3 years ago
The sandbox at a playground is 2 feet tall.The area of the base of the sandbox mis 80 square feet.How much sand does it take to
DaniilM [7]
360 square feet of sand, I think
8 0
3 years ago
Compute the volume of a sphere with a radius of 12 inches.
dalvyx [7]
V=(4pr^3)/3 if r=12

V=2304p in^3
3 0
3 years ago
X ⋅ x ⋅ x ⋅ x ⋅ x = ? 5x x(x + 5) x + 5 x5
vampirchik [111]

Answer

x.x.x.x.x = 5x

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Other questions:
  • How do you factor 5x^2 = 10x
    6·2 answers
  • You only friend buys two fruit smoothies and leave a tip. You split the total in your half comes to $3.60. What percent tip in d
    6·2 answers
  • Ed is on a road trip. He has already traveled 242 miles and is driving at a rate of 63 miles per hour. Which equation could be u
    9·1 answer
  • What is the sum 3/5 3/7
    6·1 answer
  • Maia's calculator displays a number as 9.125 E10. What is this number in standard form?
    14·2 answers
  • The table shows the outputs, y, for different inputs, x: Input (x) 3 7 11 15 Output (y) 4 6 8 10 Part A: Do the data in this tab
    13·1 answer
  • ????? pls help hdjsjddh​
    15·1 answer
  • Writing What is the diameter of a circle with a circumference of 11.277 ft? Use pencil and paper.
    15·1 answer
  • 1+1(2)-5+96-4(67+9)+59+10
    6·1 answer
  • Joe saved $8000 in his bank account. His account interest rate is 2.1%. What will his bank account balance be after 6 years?
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!