Question

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 SDStrawberry Drink 10 537 22Cola 10 559 17Required:a. Does the data suggest that the extra carbonation of cola results in a higher average compression strength? Base your answer on a P-value.b. State the relevant hypotheses. c. Compute the test statistic value and find the P-value.d. State the conclusion in the problem context.e. What assumptions are necessary for your analysis?1. The distributions of compression strengths are approximately normal.2. The distributions of compression strengths have equal means. 3. The distributions of compression strengths are the same.4. The distributions of compression strengths have equal variances.

Answer 1

Answer:

Explained below.

Step-by-step explanation:

In this case we need to test whether the extra carbonation of cola results in a higher average compression strength.

(a)

The hypothesis for the test can be defined as follows:

H₀: The extra carbonation of cola does not results in a higher average compression strength, i.e. μ₁ - μ₂ = 0.

Hₐ: The extra carbonation of cola results in a higher average compression strength, i.e. μ₁ - μ₂ < 0.

(c)

Since the population standard deviations are not provided, we would use the t-test for difference between means.

The test statistic is:

$t=\frac{\bar x_{1}-\bar x_{2}}{\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}}$

  $=\frac{537-559}{\sqrt{\frac{22^{2}}{10}+\frac{17^{2}}{10}}}\\\\=\frac{-22}{8.792}\\\\=-2.502$

The test statistic value is -2.502.

(c)

Compute the p-value as follows:

$p-value=P(t_{16}$

*Use a t-table.

The p-value of the test is 0.012.

(d)

The significance level of the test is, c

p-value = 0.012 < α = 0.05.

The null hypothesis will be rejected.

Conclusion:

The data suggest that the extra carbonation of cola results in a higher average compression strength.

(e)

The assumption necessary for the analysis is:

The distributions of compression strengths are approximately normal.

The correct option is (A).