Becky is planning a 2 100-mile trip to St. Louis to visit a college. Her car averages 30 miles per gallon

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

Let a = {1, 2, 3, 4, 5} b = {1, 3, 5} c = {4, 6}. find the cardinality of the given set. 33. n(a) 34. n(b) 35. n(a ⋃

bearhunter [10]

1) n(a) = 5

The cardinality of a set is the number of elements in that set. So, you simply need to count how many elements belong to the set, and the answer is 5

2) n(b) = 3

Simlarly, in this case you need to count how many elements belong to the set, the answer is 3

3) n(a ⋃ c) = 6

The union of two set is a set composed by all the elements belonging to either one of the sets, with no repetitions. So, since the first set contains all numbers from 1 to 5, the second set contains a 4, which however already belonged to the first set, but also a 6, which is added in the union. So, a ⋃ c = {1,2,3,4,5,6}, and thus n(a ⋃ c)=6.

4) n(a ⋂ c) = 1

The intersection of two sets is a set composed by the elements belonging to both sets. So, 1,2,3 and 5 don't belong to the intersection, because they belong to the first set alone, while 6 doesn't belong to the intersection because they don't belong to the first one. So, a ⋂ c = {4}, and thus n(a ⋃ c)=1.

4 0

3 years ago

Read 2 more answers

What is 55-22 asap I USED MY HANDS BUT -_-

jok3333 [9.3K]

Answer:

33 there you go

Step-by-step explanation:

4 0

2 years ago

A = 6 - 35 B = 3x + 53 Solve for x then find the measure of A.

11111nata11111 [884]

Answer:

A = 73°

Step-by-step explanation:

A + B = 180 because of alternating interior angles

Substitute each angle

6x - 35 + 3x + 53 = 180

9x + 18 = 180

9x = 162

x = 18

Substitute A

A = 6x - 35

A = 108 - 35

A = 73

Hope this helps

Have a great day!

6 0

2 years ago

Find 6% of $5.65 and round the product to the nearest cent.

Leviafan [203]

Answer:

$0.34

Step-by-step explanation:

a = p*w

a = .06*5.65

a = 0.339

rounded = 0.34

hope this helps :)

8 0

3 years ago