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
Zanzabum
2 years ago
5

An article includes the accompanying data on compression strength (lb) for a sample of 12-oz aluminum cans filled with strawberr

y drink and another sample filled with cola
Beverage SampleSize SampleMean SampleSD
Strawberry Drink 10 537 22
Cola 10 559 17.
Assume the two populations are normal. Does the data suggest that the extra carbonation of cola results in a higher average compression strength?
Mathematics
1 answer:
Veseljchak [2.6K]2 years ago
5 0

Answer:

<em>The calculated value |t| = 2.375 > 2.1009  at 0.05 level of significance</em>

<em>Null hypothesis is rejected </em>

<em>Alternative hypothesis is accepted</em>

<em>The extra carbonation of cola results in a higher average compression strength</em>

<u><em /></u>

Step-by-step explanation:

<u><em>Step(i):-</em></u>

<em>Given data</em>

<em>First sample size (n₁) = 10 </em>

<em>mean of the first sample(x₁⁻) = 537</em>

<em>standard deviation of the first sample (S₁) = 22</em>

<em>second sample size (n₂) = 10 </em>

<em>mean of the second sample (x₂⁻) = 559</em>

<em>standard deviation of the second sample (S₂) = 17</em>

<u><em>Step(ii)</em></u><em>:-</em>

<u><em>Null hypothesis : H₀:</em></u><em>- The extra carbonation of cola results in a lower average compression strength</em>

<u>Alternative Hypothesis :H₁</u>

<em>The extra carbonation of cola results in a higher average compression strength</em>

<u><em>Step(iii)</em></u><em>:-</em>

<em>By using student's t -test for difference of means</em>

<u><em>Test statistic</em></u>

<em>       </em>t = \frac{x^{-} _{1}-x^{-} _{2}  }{\sqrt{S^{2} (\frac{1}{n_{1} }+\frac{1}{n_{2} }  } )}<em />

<em>  where </em>

<em>     </em>S^{2}  = \frac{n_{1}S^{2} _{1} + n_{2} S_{2} ^{2}  }{n_{1}+n_{2} -2 }<em />

<em>    </em>S^{2}  = \frac{10(22)^{2}  + 10 (17) ^{2}  }{10+10 -2 } = \frac{ 7730}{18} = 429.4<em />

<em>    </em>t = \frac{537-559 }{\sqrt{429.4 (\frac{1}{10 }+\frac{1}{10 }  } )}<em />

<em>   t =  -2.375</em>

<em>|t| = |-2.375| = 2.375</em>

<em>Degrees of freedom</em>

<em>γ = n₁+n₂ -2 = 10+10-2 =18</em>

<em />t_{\frac{\alpha }{2} ,n-1}=t_{(\frac{0.05}{2} ,18)} = t_{(0.025,18)}}=2.1009<em />

<em>The calculated value |t| = 2.375 > 2.1009  at 0.05 level of significance</em>

<em>Null hypothesis is rejected </em>

<em>Alternative hypothesis is accepted</em>

<u><em>Final answer:-</em></u>

<em>The extra carbonation of cola results in a higher average compression strength</em>

<u><em /></u>

<em />

<em> </em>

<em />

You might be interested in
NEED HELP BRANLIEST TO FIRST ANSWER
Juliette [100K]

Answer:

B

Step-by-step explanation:

3 0
3 years ago
Find X.<br> Round to the nearest tenth.<br><br> Law of Cosines : c2 = 22 + b2 - 2ab cos C
fiasKO [112]

Answer:

70.5°

Step-by-step explanation:

22² = (20)²+(18)² - 2(20)(18) cos X

484 = 400 + 324 - 720 cos X

-240 = -720 cosx

1/3 = cos X

cos^{-1}(\frac{1}{3}) = X

X = 70.52877937

7 0
2 years ago
Given: Q = 7m + 3n, R = 11 - 2m, S = n + 5, and T = -m - 3n + 8.
Oxana [17]

Answer:

6m + n + 2

Step-by-step explanation:

[7m + 3n - 11 - 2m] + [n + 5 - -m - 3n + 8]

[5m + 3n - 11] + [n + 5 + m - 3n + 8]

5m + 3n - 11 + (-2n + 13 + m)

5m + 3n - 11 - 2n + 13 + m

6m + n + 2

3 0
3 years ago
(2 x 10^2)(4 x 10^3)
yKpoI14uk [10]

Answer:

800000x^2

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
The cylinder shown has a radius of 3 inches. The height is three times the radius. Find the volume of the cylinder. Round your s
MrRa [10]

Answer:

254.5 Inches Cubed

Step-by-step explanation:

Formula for Finding the Volume of a Cylinder: V=\pi r^2h

The radius is 3 inches.

r=3

The height is three times the radius.

Multiply the radius by three to get the height.

h=3*3\\h=9

The height is 9 inches.

Use the formula to find the volume.

\pi (3)^29= \pi (9)9=81\pi

The exact volume is 81\pi inches cubed.

81 * \pi ≈ 254.47

254.47 ≈ 254.5

The volume of the cylinder should be about 254.5 inches cubed.

3 0
3 years ago
Other questions:
  • Is the square root of 10 rational
    13·1 answer
  • I need help with this
    13·1 answer
  • 1/2 + 1/3= whats the answer
    12·2 answers
  • Consider the following results from the last ten periods of student enrollment forecast by the Operations Management department
    13·1 answer
  • Select the instances in which the variable described is binomial.
    13·1 answer
  • What is the answer for 25 = a+8 <br>​
    11·2 answers
  • Shanice spent half of her weekly allowance on cloths. To earn more money her parents let her clean the gutters for $7. What is h
    10·1 answer
  • I need help on this problem please
    9·1 answer
  • Can someone help me with this thank you
    14·2 answers
  • What is the value of 8-|2(-3.5)-5|
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!