In crash tests at five miles per hour, the mean bumper repair cost for 15 small cars is 576 dollars with a standard deviation of 186 dollars. In similar test of 21 midsize cars, the mean bumper repair cost is 700 dollars with a standard deviation of 257 dollars. Conduct a hypothesis test based on this sample data, with a = 1%. Answer the question, is the mean bumper repair cost less for small cars than it is for midsize cars?
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Here we are given that in crash tests at five miles per hour, the mean bumper repair cost for 15 small cars is 576 dollars with a standard deviation of 186 dollars. In similar test of 21 midsize cars, the mean bumper repair cost is 700 dollars with a standard deviation of 257 dollars.
That is ,
Sample sizes for small cars and midsize cars is ,
n1 = 15.
n2 = 21.
Sample means for small cars and midsize cars is ,
x̅1 = 576 dollars.
x̅2 = 700 dollars.
Sample standard deviations for small cars and midsize cars is ,
s1 = 186 dollars.
s2 = 257 dollars.
Given level of significance , α = 1% or 0.01 (in decimal).
It is asked about,
- State the hypotheses.
- The correct symbol for the mean of the sampling distribution.
- The value for the mean of the sampling distribution.
It is asked about hypotheses.
Claim : The mean bumper repair cost is less for small cars than it is for midsized cars.
Null hypotheses : The mean bumper repair cost for small cars is equal to the mean bumper repair cost for for midsize cars.
Symbolically it can be written as , Ho : µ1 -µ2 = 0.
Alternative hypotheses : The mean bumper repair cost for small cars is less than the the mean bumper repair cost for for midsize cars.
Symbolically it can be written as , Ho : µ1 -µ2 < 0
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