It is advertised that the average braking distance for a small
car traveling at 70 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 37 small
cars at 70 miles per hour and records the braking distance. The
sample average braking distance is computed as 111 feet. Assume
that the population standard deviation is 21 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.)
Find the p-value.
p-value < 0.01
c. Use α = 0.10 to determine if the
average breaking distance differs from 120 feet.
Solution :
= 120
= 111
=21
n = 37
This is the two tailed test .
The null and alternative hypothesis is ,
H0 : = 120
Ha : 120
Test statistic = z
= ( - ) / / n
= (111-120) / 21 / 37
= -2.61
P (Z < -2.61 ) = 0.0091
P-value = 0.01
= 0.10
p=0.01< 0.10
Reject the null hypothesis .
There is enough evidence to claim that the population mean μ is different than 120, at the 0.10 significance level.
It is advertised that the average braking distance for a small car traveling at 70 miles...
It is advertised that the average braking distance for a small car traveling at 70 miles per hour equals 122 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 33 small cars at 70 miles per hour and records the braking distance. The sample average braking distance is computed as 115 feet. Assume that the population standard deviation is 24 feet. a. State the null and the alternative hypotheses...
It is advertised that the average braking distance for a small car traveling at 70 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 32 small cars at 70 miles per hour and records the braking distance. The sample average braking distance is computed as 115 feet. Assume that the population standard deviation is 21 feet. (You may find it useful to reference the...
It is advertised that the average braking distance for a small car traveling at 70 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 35 small cars at 70 miles per hour and records the braking distance. The sample average braking distance is computed as 113 feet. Assume that the population standard deviation is 22 feet. (You may find it useful to reference the...
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