Question 1 of 10

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

2 years ago

Plz help me 75 points for the 2 questions!!!

liraira [26]

Answer:

The system of equations:

2x + 7y = -11
3x + 5y = -22

Solve by elimination.

Triple the first equation, double the second one, subtract the second from the first and solve for y:

3(2x + 7y) - 2(3x + 5y) = 3(-11) - 2(-22)
6x + 21y - 6x - 10y = -33 + 44
11y = 11
y = 1

Find x:

2x + 7*1 = -11
2x = -11 - 7
2x = -18
x = -9

The solution is:

x = -9, y = 1

Simplifying in steps:

8u - 29 > -3(3 - 4u)
8u - 29 > - 9 + 12u
12u - 8u < -29 + 9
4u < -20
u < -5

3 0

3 years ago

A rugby team played six games.

Schach [20]

Step-by-step explanation:

mean score means the sum of all 6 scores divided by the number of games : 6.

sum6/6 = 15

sum6 = 15×6 = 90

(sum6 + x)/7 = 16

sum6 + x = 16×7 = 112

90 + x = 112

x = 22

they scored 22 points in the 7th game.

3 0

2 years ago

The table shows a proportional relationship between the number of stars Roberto collects in a game and his total points. A row o

maks197457 [2]

Answer:

1) 20 stars; 30 points.

2) 28 stars, 42 points.

3) 38 stars, 57 points.

Step-by-step explanation:

<h3> The missing table is attached.</h3>

Let be "x" the numbers of stars Roberto collects and "y" his total points.

The proportional relationship has this form:

$y=kx$

Where "k" is the constant of proportionality.

We can choose the point $(8,12$ ) from the table, where:

$x=8\\y=12$

Substituting these values into $y=kx$ and solving for "k", we get:

$12=k(8)\\\\\frac{12}{8}=k\\\\k=1.5$

Knowing the value of "k", we determine that the following Numbers of stars and the Total points could be used as the missing values in the table:

1) For $x=20$ :

$y=(1.5)(20)=30$

2) For $x=28$ :

$y=(1.5)(28)=42$

3) For $x=38$ :

$y=(1.5)(38)=57$

4 0

3 years ago

Read 2 more answers

7g = -84 ; g = - 12 due in 10 min WHAT IS UP WITH THESE TIMED MATH TESTS T^T

dolphi86 [110]

Step-by-step explanation:

7 (-12) = -84

it's literally -84

7 0

2 years ago