Answer:
Based on the results of the one-sample t-test, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the true mean impurity rate of the shipment is greater than 0.6% at the 95% level. Therefore, the shipment might be impure and does not meet the regulations.
Step-by-step explanation:
To determine whether this shipment might be impure at the 95% level, we need to perform a hypothesis test.
Null hypothesis: The true mean impurity rate of the shipment is equal to or less than 0.6%.
Alternative hypothesis: The true mean impurity rate of the shipment is greater than 0.6%.
We can use a one-sample t-test to test this hypothesis. The test statistic is calculated as:
⇒ t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))
Plugging in the values we have:
⇒ t = (7.2 - 6) / (1 / sqrt(12)) = 3.266
Using a t-distribution table with 11 degrees of freedom (12 samples - 1), and a significance level of 0.05, the critical value for a one-tailed test is 1.796.
Since our calculated t-value of 3.266 is greater than the critical value of 1.796, we reject the null hypothesis. This means that there is sufficient evidence to suggest that the true mean impurity rate of the shipment is greater than 0.6% at the 95% level. In other words, the shipment might be impure and does not meet the regulations.