Question

Please help with this problem

12. Identify an appropriate test for each of the following situations: (a) A random sample of workers is taken from each of 3 factories and the number of overdme hours (b) A chemist is evaluating a new method for determining the percentage content of an element in a (c) Researchers collected intelligence test scores on twins, one of whom was raised by the natural (d) Two methods for determining the percentage of iron in ore samples were compared by splitting each (e) In a famous experiment to assess the efficiency of aspirin in preventing heart attacks, 22,000 healthy worked for each worker is recorded. The purpose of the study is to examine the relationship between factory and hours of overtime worked. sample. She obtains a specimen of known content and makes 10 measurements of the percentage content of the element. She wants to compare her measurements to the known content parents and one of whom was raised by foster parents. They are interested in knowing whether there is an advantage in resulting intelligence scores for children raised by their natural parents. of 87 ore samples into two parts. One part was then measured using method 1, and the other part was measured using method 2. middle-aged men were divided into two equal groups, one of which was given a daily dose of aspirin and one of which was given a placebo that looked and tasted identical to the aspirin. At the time that the experiment was halted, numbers of members in each group who had heart attacks are recorded. (f) A telephone company is trying to decide whether some new lines in a large community should be installed underground. Because a small surcharge will be added to telephone bills to pay for the extra installation costs, the company has decided to survey customers and proceed only if the survey strongly indicates that more than 60% of all customers favor underground installation.

Answer 1

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

Hi p> 60

Please comment in case if you need more explanation.