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:
<em>H</em>₀: The extra carbonation of cola does not results in a higher average compression strength, i.e. <em>μ</em>₁ - <em>μ</em>₂ = 0.
<em>Hₐ</em>: The extra carbonation of cola results in a higher average compression strength, i.e. <em>μ</em>₁ - <em>μ</em>₂ < 0.
(c)
Since the population standard deviations are not provided, we would use the t-test for difference between means.
The test statistic is:
The test statistic value is -2.502.
(c)
Compute the <em>p</em>-value as follows:
*Use a <em>t</em>-table.
The <em>p</em>-value of the test is 0.012.
(d)
The significance level of the test is, <em>c</em>
<em>p</em>-value = 0.012 < <em>α</em> = 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).