## Answers

12)a)ANOVA. There are actually three groups( factories) of overtimes and the hypothesis of interest (null hypothesis) is the mean overtimes are equal for all the three groups against the alternative that atleast one factory has a significant mean overtime. And if the null hypothesis is rejected we do a post hoc test to test which group means are significant

b)One sample t test would be appropriate where the known content is taken as the population mean and the average sample measurements is the sample mean

c) Since the twins share some common charateristics, the samples are not independent. Since there was no mentioning regarding the population or the sample size application of paired t test can not be justified. so a non parametric alternative such as Wilcoxon **paired** signed rank **test** and the **paired** sign **test**.

May be appropriate here.

d) A two sample t test would be appropriate to test whether the measurement by the two methods differ significantly.

e) chi-square test for independence or association can be used to test whether the placebo group is more likely to develop heart attacks.

f)One sample proportion test is the most appropriate test where the alternative is a one tailed hypothesis ie

Please comment in case if you need more explanation.