Suppose Matt wants to test the claim that the mean pulse rate of adult males is equal to 69 bpm, since he expects it to be lower
1 answer:
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Answer:
a and b are perpendicular to each other, as are b and d, b and g
Step-by-step explanation:
To check whether two vectors are perpendicular to each other, we need the angle between these vectors to be 90 degrees.
We can find the angle between to vectors a and b from the following relation:
The cosine of the angle between two vectors is equal to the dot product of this vectors divided by the product of vector magnitude.
So
cos(90) = 0, so when the dot product between vectors a and b is 0, it means that these vectors are perpendicular to each other.
Now, for your exercise, let's compute the dot product between these vectors.
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a.b = (3,1,-1).(1,1,4) = 3+1-4 = 0
So a and b are perpendicular to each other.
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a.c = (3,1,-1).(1,3,1) = 3+3-1 = 5
a and c are not perpendicular to each other.
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a.d = (3,1,-1).(-1,-3,1) = -3-3-1 = -7
So not perpendicular
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a.g = (3,1,-1).(-3,-1,1) = -9-1-1 = -11
Not
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b.c = (1,1,4).(1,3,1) = 1+3+4 = 8
Not
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b.d = (1,1,4).(-1,-3,1) = -1 -3 +4 = 0
b.d = 0, so b and d are perpendicular to each other
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b.g = (1,1,4).(-3,-1,1) = -3-1+4 = 0
b.g = 0, perpendicular
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c.d = (1,3,1).(-1,-3,1) = -1-9+1 = -9
No
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c.g = (1,3,1).(-3,-1,1) = -3-3+1 = -5
No
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d.g = (-1,-3,1).(-3,-1,1) = 3+3+1 = 7
No
Answer:
Type I error: Concluding that mean mileage is less than 32 miles per hour when actually it is greater than or equal to 32 miles per gallon.
Step-by-step explanation:
We are given the following in the question:
Hypothesis:
Mean mileage for the Carter Motor Company's new sedan
We can design the null hypothesis and alternate hypothesis as:
Type I error:
- It is the false positive error.
- It is the error of rejection a true hypothesis.
Type II error:
- It is the false negative error.
- It is the non rejection of a false null hypothesis.
Thus, type I error for the given hypothesis is concluding that mean mileage is less than 32 miles per hour when actually it is greater than or equal to 32 miles per gallon.
Type II error would be concluding that mean mileage is greater than or equal to 32 miles per gallon when actually it is less than 32 miles per gallon.