9-16 A car manufacturer is trying to develop a new sports car. Engineers are hoping that the average amount of time that the car takes to go from 0 to 60 miles per hour is below 6 seconds. The manufacturer tested 12 of the cars and clocked their performance times. Three of the cars clocked in at 5.8 seconds, 5 cars at 5.9 seconds, 3 cars at 6.0 seconds, and 1 car at 6.1 seconds. At the 5% level of significance, test if the new sports car is meeting its goal to go from 0 to 60 miles per hour in less than 6 seconds. Assume a normal distribution for the analysis. (You may find it useful to reference the appropriate table: z table or t table)
a. Specify the competing hypotheses to test this
belief.
H_{0}: μ = 6; H_{A}: μ ≠ 6
H_{0}: μ ≥ 6; H_{A}: μ < 6
H_{0}: μ ≤ 6; H_{A}: μ > 6
b. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)
c. 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
d. Use α = 0.05 to test if the new sports car is meeting its goal.
(Reject Ho or Do not reject Ho) at the 5% significance, we (can, can not) conclude that the average clock time of all cars is less than 6 seconds.
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