Can someone help me with this problem ASAP please.

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

Kate purchased a car for $23,000. It will depreciate by a rate of 12% a year. What is the value of the car in 4 years. *

Ivan

Answer:

$13,793

Step-by-step explanation:

Kate purchased a car for $23,000. It will depreciate by a rate of 12% a year. What is the value of the car in 4 years. *

The formula for Depreciation rate =

y = a(1 - r) ^t

Where

y = Value of the car after t years

a = Initial value of the car = $23,000

t= time in years = 4 years

r = Depreciation rate = 12% = 0.12)

y = $23000 (1 - 0.12)⁴

y = $13792.99328

Approximately = $13,793:

3 0

3 years ago

Draw a net for each of the following shapes:

Margarita [4]

A. You would start off by a rectangle in the middle, then you would place to squares on the bottom and top if the rectangle. After you've done that, you place two rectangles (Same size as the original) on both sides of the original rectangle. Finally you add a rectangle (Same size) to either ends of the secondary rectangles. It should look like this.

B. You would start off with a rectangle in the middle, then you would add 2 equilateral triangles to the top and bottom of the rectangle. After that, you Simply put 2 rectangles (Same size as the original) on both sides of the rectangle. It should look something like this.

C. To make a pyramid, it's actually quite simple. You would start off with a square in the middle, and then place equilateral triangles on ALL sides of the square. It should look something like this.

I hope this helped ^^