A auto maker is interested in information about how long transmissions last. A sample of transmissions are run constantly and the number of miles before the transmission fails is recorded. The auto maker claims that the transmissions can run constantly for over 150,000 miles before failure. The results of the sample are given below. Miles (1000s of miles) Mean 150.7 Variance 4.661 Observations 46 Hypothesized Mean df 150 45 t Stat 2.185 p = Ex 1.234 P(T<=t) one-tail t Critical one-tail 0.017 1.679 -3 -2 -1 P(T<=t) two-tail t Critical two-tail 0.034 2.014 t = Ex: 1.234 Confidence Level(95.0%) 0.641 What condition is met for the use of a t-distribution? Pick n = Ex: 5 I = Ex: 1.2 Degrees of freedom = Ex: 5 8 = Ex: 1.234
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.
![CHALLENGE ACTIVITY
6.2.2: Relating confidence intervals to hypothesis testing (one sample).
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A auto maker is interested in information about how long transmissions last. A sample of transmissions are run
constantly and the number of miles before the transmission fails is recorded. The auto maker claims that the
transmissions can run constantly for over 150,000 miles before failure. The results of the sample are given below.
Miles (1000s of miles)
Mean
150.7
Variance
4.661
Observations
46
Hypothesized Mean
150
df
45
t Stat
2.185
p= Ex 1.234
P(T<=t) one-tail
t Critical one-tail
0.017
1.679
-3
-2
-1
1
P(T<=t) two-tail
t Critical two-tail
0.034
2.014
t = Ex: 1.234
Confidence Level(95.0%) 0.641
What condition is met for the use of a t-distribution? Pick
n = Ex: 5
x = Ex: 1.2
Degrees of freedom= Ex: 5
8 = Ex: 1.234](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F52bd3cfe-3c9b-40ce-8732-3b0b81ba9280%2F0fd06d03-b37a-4395-aa68-32f8d1574dfe%2Fah2cigf_processed.jpeg&w=3840&q=75)
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