For the multiple choice questions, circle the best answer:
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.
For the multiple choice questions, circle the best answer:
(a) In which of the following scenarios is a paired design not appropriate?
A. Comparison of two different brands of deodorant, where each person tests one brand in one armpit and one brand in the other armpit.
B. Comparison of two different brands of deodorant, where each person tests only one brand.
C. Comparison of a cream and an ointment in the treatment of a rash, where each person places the cream on one arm, and the ointment on the other.
D. Comparison of a cream and an ointment in the treatment of a rash, where each person applies the ointment to half of a rash and the cream to the other half.
(b) We can make statistical inferences about populations even if we do not know the true population distribution because ...
A. Regardless of the true population distribution, all we need for a test statistic is the sample
means and their standard deviations (or estimates of the standard deviations), and we can get these from our samples.
B. A sample size ≥ 30 guarantees Normality of the sample
C. Regardless of the true population distribution, the Central Limit Theorem guarantees Normality of the sample mean as sample size goes to infinity.
D. Random sampling guarantees a representative sample regardless of the true population distribution.
(c) A random sample of 600 adults is taken to estimate a population proportion among US adults. If the researchers wanted to decrease the width of the confidence interval, they could
A. increase the
B. decrease the size of the population.
C. increase the size of the population.
D. decrease the size of the sample.
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