Consider a one-sample t-test with N(u, o2) data with Ho: H =0 versus HA: µ >0. It is well known that the test statistic in this case is T = X/(S//n), where X is the sample mean, S is the sample standard deviation, and n is the sample size. Under the null hypothesis, T~ tn-1.
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.
![(b) Write a short paragraph where you discuss the following points.
(i) Describe the shapes of the histograms. In which case the histogram of p-values looks flat and
uniformly distributed over the interval [0, 1]?
(ii) Using the histograms, compare the chances of observing a p-value less than a = 0.05. How the
chances change depending on µ?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5b0702a9-19e2-4386-bbd9-e0ccdec0e93e%2F34b24242-7e50-48f2-bf41-06fbaeab21f3%2F7pv97aw_processed.jpeg&w=3840&q=75)
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