## Related questions with answers

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.

Solution

VerifiedThe goal of this task is to construct null and alternative hypotheses for testing whether a new sports car meets its goal of reaching $0$ to $60$ miles per hour in less than $6$ seconds.

- $n = 12$ of new cars being tested
- $3$ cars ran $5.8$ seconds
- $5$ cars ran $5.9$ seconds
- $3$ cars ran $6$ seconds
- The $1$ car ran $6.1$ seconds

We need to determine the value of the test statistic, $p-$ value, and test hypotheses at the level of $5 \%$ significance.

Suppose this is a normal distribution.

**Which steps do we need to follow to construct hypotheses?**

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