It is advertised that the average braking distance for a small
car traveling at 65 miles per hour equals 120 feet. A
transportation researcher wants to determine if the statement made
in the advertisement is false. She randomly test drives 36 small
cars at 65 miles per hour and records the braking distance. The
sample average braking distance is computed as 114 feet. Assume
that the population standard deviation is 22 feet. (You may
find it useful to reference the appropriate table: z table
or t table)
a. State the null and the alternative hypotheses
for the test.
H0: μ = 120; HA: μ ≠ 120
H0: μ ≥ 120; HA: μ < 120
H0: μ ≤ 120; HA: μ > 120
b. Calculate the value of the test statistic and
the p-value. (Negative value should be indicated
by a minus sign. Round intermediate calculations to at least 4
decimal places and final answer to 2 decimal
places.)
test statistic=
Find the p-value.
p-value < 0.01
0.01 ≤ p-value < 0.025
0.025 ≤ p-value < 0.05
0.05 ≤ p-value < 0.10
p-value ≥ 0.10
c. Use α = 0.01 to determine if the
average breaking distance differs from 120 feet.
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different from 120 feet.
a) Option-A) H0: μ = 120; HA: μ ≠ 120
b) Test statistic
= -1.64
P-value = 2 * P(Z < -1.64) =2 * 0.0505 = 0.1010
Option-D) p-value ≥ 0.10
c) since p-value is not less than 0.01, we should not reject the null hypothesis.
No, the average breaking distance is not different from 120 feet
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