An article includes the accompanying data on compression strength (lb) for a sample of 12-oz aluminum cans filled with strawberry drink and another sample filled with cola. Beverage Sample Size Sample Mean Sample SD Strawberry Drink 10 535 24 Cola 10 559 15 Does the data suggest that the extra carbonation of cola results in a higher average compression strength? Base your answer on a P-value. (Use ? = 0.05.) State the relevant hypotheses. (Use ?1 for the strawberry drink and ?2 for the cola.) H0: ?1 − ?2 = 0 Ha: ?1 − ?2 ≥ 0H0: ?1 − ?2 = 0 Ha: ?1 − ?2 ≠ 0 H0: ?1 − ?2 = 0 Ha: ?1 − ?2 < 0H0: ?1 − ?2 = 0 Ha: ?1 − ?2 > 0 Calculate the test statistic and determine the P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.) t = P-value = State the conclusion in the problem context. Reject H0. The data suggests that cola has a higher average compression strength than the strawberry drink.Reject H0. The data does not suggest that cola has a higher average compression strength than the strawberry drink. Fail to reject H0. The data suggests that cola has a higher average compression strength than the strawberry drink.Fail to reject H0. The data does not suggest that cola has a higher average compression strength than the strawberry drink. What assumptions are necessary for your analysis? The distributions of compression strengths are the same.The distributions of compression strengths have equal means. The distributions of compression strengths have equal variances.The distributions of compression strengths are approximately normal.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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An article includes the accompanying data on compression strength (lb) for a sample of 12-oz aluminum cans filled with strawberry drink and another sample filled with cola.

Beverage	Sample Size	Sample Mean	Sample SD
Strawberry Drink	10	535	24
Cola	10	559	15

Does the data suggest that the extra carbonation of cola results in a higher average compression strength? Base your answer on a P-value. (Use

? = 0.05.)

State the relevant hypotheses. (Use ?₁ for the strawberry drink and ?₂ for the cola.)

H₀: ?₁ − ?₂ = 0
H_a: ?₁ − ?₂ ≥ 0H₀: ?₁ − ?₂ = 0
H_a: ?₁ − ?₂ ≠ 0 H₀: ?₁ − ?₂ = 0
H_a: ?₁ − ?₂ < 0H₀: ?₁ − ?₂ = 0
H_a: ?₁ − ?₂ > 0

Calculate the test statistic and determine the P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.)

t	=
P-value	=

State the conclusion in the problem context.

Reject H₀. The data suggests that cola has a higher average compression strength than the strawberry drink.Reject H₀. The data does not suggest that cola has a higher average compression strength than the strawberry drink. Fail to reject H₀. The data suggests that cola has a higher average compression strength than the strawberry drink.Fail to reject H₀. The data does not suggest that cola has a higher average compression strength than the strawberry drink.

What assumptions are necessary for your analysis?

The distributions of compression strengths are the same.The distributions of compression strengths have equal means. The distributions of compression strengths have equal variances.The distributions of compression strengths are approximately normal.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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