To answer your question, I will perform an Analysis of Variance (ANOVA) test to determine if the mean mixing times for the machines produced by the four manufacturers are equal, given a significance level of $\alpha = 0.05$. Let me calculate it for you. numpy as np import scipy.stats as stats

Data extracted from the table

manufacturer_A = [25, 23, 21, 23] manufacturer_B = [23, 21, 23, 24] manufacturer_C = [25, 25, 25, 21] manufacturer_D = [22, 23, 23, 22]

Perform one-way ANOVA test

f_statistic, p_value = stats.f_oneway(manufacturer_A, manufacturer_B, manufacturer_C, manufacturer_D)

f_statistic, p_valueThe ANOVA test results are:

• $F$-statistic: 0.806
• $p$-value: 0.514

Since the $p$-value ($0.514$) is greater than the significance level ($\alpha = 0.05$), we fail to reject the null hypothesis ($H_0$). This means there is insufficient evidence to conclude that the mean mixing times for the machines are different. The machines can be considered to have equal mean mixing times.

Correct Answer:

The data provide insignificant evidence against $H_0$: Equal means at $p$-value 0.514. The machines are considered equal.

Do you want further explanation on the ANOVA test or its interpretation? Here are 5 related questions for deeper understanding:

1. What does the $F$-statistic represent in ANOVA?
2. How do we calculate the $F$-statistic manually?
3. What assumptions must be met to perform an ANOVA test?
4. How would we interpret the result if the $p$-value was less than 0.05?
5. Can ANOVA be used for more than 4 groups, and how does that affect the test?

Tip: Always check the assumptions of ANOVA (e.g., normality and equal variances) before interpreting results for accuracy!