MathsWatch Question Please Help

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

Veseljchak [2.6K]

Answer:

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

Null hypothesis is rejected 

Alternative hypothesis is accepted

The extra carbonation of cola results in a higher average compression strength

Step-by-step explanation:

Step(i):-

Given data

First sample size (n₁) = 10

mean of the first sample(x₁⁻) = 537

standard deviation of the first sample (S₁) = 22

second sample size (n₂) = 10

mean of the second sample (x₂⁻) = 559

standard deviation of the second sample (S₂) = 17

Step(ii):-

Null hypothesis : H₀:- The extra carbonation of cola results in a lower average compression strength

Alternative Hypothesis :H₁

The extra carbonation of cola results in a higher average compression strength

Step(iii):-

By using student's t -test for difference of means

Test statistic

  $t = \frac{x^{-} _{1}-x^{-} _{2} }{\sqrt{S^{2} (\frac{1}{n_{1} }+\frac{1}{n_{2} } } )}$ 

 where 

  $S^{2} = \frac{n_{1}S^{2} _{1} + n_{2} S_{2} ^{2} }{n_{1}+n_{2} -2 }$ 

  $S^{2} = \frac{10(22)^{2} + 10 (17) ^{2} }{10+10 -2 } = \frac{ 7730}{18} = 429.4$ 

  $t = \frac{537-559 }{\sqrt{429.4 (\frac{1}{10 }+\frac{1}{10 } } )}$ 

 t = -2.375

|t| = |-2.375| = 2.375

Degrees of freedom

γ = n₁+n₂ -2 = 10+10-2 =18

 $t_{\frac{\alpha }{2} ,n-1}=t_{(\frac{0.05}{2} ,18)} = t_{(0.025,18)}}=2.1009$ 

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

Null hypothesis is rejected 

Alternative hypothesis is accepted

Final answer:-

The extra carbonation of cola results in a higher average compression strength

 

5 0

3 years ago

Use the distributive property to simplify the expressions. 1B. -3(9x-q) 2B. 2(12+5p) 3b. -7(-8y+7) 4b. 10(2+7c) 5b. -8(7+11k) 6b

Debora [2.8K]

1B: -3(9x-q)
-27x + 3q

Step 1: Distribute the -3 to the 9x to get -27x.
Step 2: Distribute the -3 to the -q.

2B: 2(12+5p)
24 + 10p

Step 1: Distribute the 2 to the 12 to get 24.
Step 2: Distribute the 2 to the 5p to get 10p.

3B: -7(-8y+7)
56y - 49

Step 1: Distribute the -7 to the -8y to get 56y.
Step 2: Distribute the -7 to the 7 to get -49.

4B: 10(2+7c)
20 + 70c

Step 1: Distribute the 10 to the 2 to get 20.
Step 2: Distribute the 10 to the 7c to get 70c.

5B: -8(7+11k)
-56 - 88k

Step 1: Distribute the -8 to the 7 to get -56.
Step 2: Distribute the -8 to the 11k to get -88k.

6B: -(3-7u)
-1(3-7u)
-3 + 7u

Step 1: Place a 1 after the negative symbol to symbolize -1.
Step 2: Distribute the -1 to the three to get -3.
Step 3: Distribute the -1 to the -7u to get 7u.

7B: -6(5p + s)
-30p - 6s

Step 1: Distribute the -6 to the 5p to get -30p.
Step 2: Distribute the -6 to the s to get -6s.

:) :D

8 0

3 years ago

5•11+5•(-4)=5(11-4) wich property?

ludmilkaskok [199]

Answer:

Step-by-step explanation:

55

3 0

3 years ago

I need help and it’s due today

frez [133]

Answer:

5.63

Step-by-step explanation:

Angle NLM is equal to KLM - KLN.

Since KLM = 137° and KLN = 47°, NLM = °90. (Maybe it doesn't look like a right angle, but the math doesn't lie.)

Since NLM = 16y, then 90 = 16y.

Dividing both sides by 16, we find that:

y = 5.625

5 0

3 years ago

Read 2 more answers

THIS QUESTION IS WORTH 15 POINTS

ikadub [295]

Answer:

3.7

This means that the answer is past the 3 point on the number line and 3 tick marks before the 4 point.

5 0

3 years ago