It is advertised that the average braking distance for a small car traveling at
ID: 3130161 • Letter: I
Question
It is advertised that the average braking distance for a small car traveling at 75 miles per hour equals 124 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 37 small cars at 124 miles per hour and records the braking distance. The sample average braking distance is computed as 112 feet. Assume that the population standard deviation is 22 feet. Use Table 1.
Calculate the value of the test statistic and the p-value. (Negative values should be indicated by a minus sign. Round "Test statistics" to 2 decimal places. Round "p-value" to 4 decimal places.)
Repeat the test with the critical value approach. (Negative values should be indicated by a minus sign. Round your answers to 3 decimal places.)
(Round all intermediate calculations to at least 4 decimal places.)Explanation / Answer
Using tables,
a)
Formulating the null and alternative hypotheses,
Ho: u = 124
Ha: u =/ 124 [ANSWER, A]
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b)
As we can see, this is a two tailed test.
Getting the test statistic, as
X = sample mean = 112
uo = hypothesized mean = 124
n = sample size = 37
s = standard deviation = 22
Thus, z = (X - uo) * sqrt(n) / s = -3.317870471 [ANSWER]
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Also, the p value is
p = 0.0010 [ANSWER]
[If we do not round z, it is more exactly 0.0009.]
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c)
As P < 0.01, then
The average breaking distance is [significantly different different] from 124 miles. [ANSWER]
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d)
As we can see, this is a two tailed test.
Thus, getting the critical z, as alpha = 0.01 ,
alpha/2 = 0.005
zcrit = +/- 2.575829304
As |z| > 2.756, then WE REJECT HO. [ANSWER]
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