Adv Stats Blog

#1: A. The null hypothesis (H0) is that the mean breaking strength of the cookies is 70 pounds, and the alternative hypothesis (H1) is that the mean breaking strength is not 70 pounds. B. To determine if there is evidence that the machine is not meeting the manufacturer’s specifications for average strength, we would perform a hypothesis test. We would calculate a test statistic using the sample mean, population mean, standard deviation, and sample size, and then compare this test statistic to a critical value determined by the 0.05 level of significance. C. The p-value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true. It’s calculated using the test statistic and the relevant distribution (in this case, likely the t-distribution given that we’re dealing with means and a small sample size). If the p-value is less than our level of significance (0.05), we would reject the null hypothesis. D. If the standard deviation ...

 Part A: 1. The probability of Event A occurring is calculated with P(A) = 30/90, which equals approximately a 33% chance of occurring.  2. The probability of Event B occurring is calculated with P(B) = 30/90, which equals approximately a 33% chance of occurring as well.  3.  In this case, both A and B occur for 10 outcomes. So, P(A ∩ B) = 10/90 = 0.11. Therefore, P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.33 + 0.33 - 0.11 = 0.56. 4. This formula is used to calculate the probability of either event A or event B occurring. However, this formula assumes that events A and B are mutually exclusive, which means they cannot occur at the same time. If events A and B can occur at the same time, then we need to subtract the probability of both events occurring from the sum of their individual probabilities to avoid double-counting. Part B B1. The answer is True. B2. The calculation is based on Bayes’ theorem, which is a fundamental concept in probability theory and stati...