Chapter 12, Problem 36SGR

To determine

To test: The hypothesis that the average number of cars is less than 10.

Explanation of Solution

Given:

A light at an intersection is timed to let 10 car turns left each rotation.

Danny believes it is less than the 10 and tests the light.

Data is collected for 50 rotations.

Mean=9.1

Standard deviation=0.8

Danny tests 50 rotations and after collecting data for 50 rotations Danny arrives at a mean of 9.1 cars and a standard deviation of 0.8 cars.

Hence,

  $\begin{array}{l}n=50\\ \overline{x}=9.1\\ s=0.8\end{array}$

Considering the Hypothesis:

  $\begin{array}{l}{H}_o:\mu =10\\ H_1:\mu <10\end{array}$

Now, evaluating the 95% confidence interval:

  $\begin{array}{l}CI=\overline{x}\pm 1.96\left(\frac{s}{\sqrt{n}}\right)\\ =9.1\pm 1.96\left(\frac{0.8}{\sqrt{50}}\right)\\ =9.1\pm 0.22\\ =\left(8.88,9.32\right)\end{array}$

As the confidence interval does not contain 10, therefore, one can reject the null hypothesis.

That is one can find that the average number of cars is less than 10.