The quality manager at Bestiful Company is certifying a new process that must produce 95% (or better) good product before the process is considered proven. A sample of 40 containers from the process line are tested, and 93% are found to be good. (a) Formulate the appropriate hypotheses and test them using an α = 0.01 significance level. (b) Explain your results.

Let's define the hypotheses for this hypothesis test:
- Null Hypothesis (H0): The proportion of good products produced by the new process is equal to 95%.
- Alternative Hypothesis (H1): The proportion of good products produced by the new process is less than 95%.

Given that the sample size is large (n = 40) and the sample proportion of good products is p̂ = 0.93, we can use the normal approximation to the binomial distribution to conduct a hypothesis test using a z-test.

(a) Test the hypotheses using a significance level of α = 0.01.
The test statistic formula for a z-test is:
z = \frac{p̂ - p}{\sqrt{\frac{p(1-p)}{n}}}
where p is the hypothesized population proportion (0.95 in this case).

Plugging in the values:
z = \frac{0.93 - 0.95}{\sqrt{\frac{0.95(1-0.95)}{40}}}
z = \frac{-0.02}{\sqrt{\frac{0.95*0.05}{40}}}
z = \frac{-0.02}{\sqrt{\frac{0.0475}{40}}}
z = \frac{-0.02}{\sqrt{0.0011875}}
z = \frac{-0.02}{0.03446}
z = -0.58

Next, we find the critical z-value for a one-tailed test at α = 0.01 by looking up the z-value in the standard normal distribution table or using a calculator: z_{\alpha = 0.01} = -2.33

(b) Conclusion:
Since our calculated z-value (-0.58) does not fall in the rejection region (less than -2.33), we do not reject the null hypothesis.
Therefore, there is not enough evidence to conclude that the proportion of good products produced by the new process is less than 95%.

\boxed{Answer: \text{The null hypothesis is not rejected. The process is proven to produce 95\% or more good products.}}