Offices are getting more casual. Companies relax their formal dress code for many reasons: they want to attract top candidates, to create a more relaxed work environment and to allow employees to be creative with their dress, which may translate to job creativity and productivity. Two large companies, Company A and Company B, are considering whether they should relax the dress code for their office workers as well. Independently, they randomly sampled their office employees to collect their opinions, and the resulting data are provided in the table below. We are interested if the proportion of all office workers in Company A who would like their company to relax the dress code is different from the proportion of all office workers in Company B who would like their company to relax the dress code, using a 10% significance level. “Would you like your company to relax the dress code?" Group Yes No Total 1 = Company A office workers 138 146 284 2 = Company B office workers 144 96 240 Recall the Steps for Testing Hypotheses: 1) State the appropriate hypotheses (the significance level has been selected to be 10%). 2) Check the necessary assumption(s) (you may assume that you have two independent random samples). 3) Perform the appropriate test (include all supporting computations for the test statistic and p-value, and the complete sketch of the p-value). 4) Evaluate the p-value and provide a conclusion in context. Organize your answer well and use labels for your Steps 1, 2, 3, and 4.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Read the following prompt and complete question 8 and its subquestions Step 1, Step 2, Step 3, and Step 4.
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