Suppose that you need to test a program you have just written. You are assigned twelve users to test your program. Each user completes an assigned task using your program, and the time (in seconds) for the user to complete the task is recorded. The observed times are 43,51,50,48,47,55,51,33,71,53,49,49. Let yi be the time taken by the ith user, for i = 1,...,12. Then, for our observed data, we have
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.
Suppose that you need to test a program you have just written. You are assigned twelve users to test your program. Each user completes an assigned task using your program, and the time (in seconds) for the user to complete the task is recorded. The observed times are 43,51,50,48,47,55,51,33,71,53,49,49. Let yi be the time taken by the ith user, for i = 1,...,12. Then, for our observed data, we have
![2. Suppose that you need to test a program you have just written. You are assigned twelve
users to test your program. Each user completes an assigned task using your program, and
the time (in seconds) for the user to complete the task is recorded. The observed times
are 43, 51, 50, 48, 47, 55, 51, 33, 71, 53, 49, 49. Let y; be the time taken by the ith user, for
i = 1,..., 12. Then, for our observed data, we have
12
600, and
i=1
12
L(yi – 7)?
830.
i=1
Assume that Y; ~ N(u, o), for some unknown u and o.
(a) Compute a 95% confidence interval for u from the observed data.
(b) Compute a 90% confidence interval for o from the observed data.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc06dfd6c-f220-41b1-93b5-8431df0a87f2%2F1dcc5a9e-987c-49c0-a055-3d8784e28440%2F65chzpsh_processed.png&w=3840&q=75)
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