Respuesta :
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:
[tex]t=\frac{\bar x_{1}-\bar x_{2}}{\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}}[/tex]
[tex]=\frac{537-559}{\sqrt{\frac{22^{2}}{10}+\frac{17^{2}}{10}}}\\\\=\frac{-22}{8.792}\\\\=-2.502[/tex]
The test statistic value is -2.502.
(c)
Compute the p-value as follows:
[tex]p-value=P(t_{16}<-2.052)=0.012[/tex]
*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).
