Question

The average number of accidents at controlled intersections per year is 4.3. Is this average less for intersections with cameras installed? The 43 randomly observed intersections with cameras installed had an average of 3.7 accidents per year and the standard deviation was 1.47. What can be concluded at the αα = 0.01 level of significance?

Can you please explain the steps of how to obtain the P value and test statistic using a graphing calculator?

Answer 1

n = 43

The test hypothesis is

Now, the value of test static can be found out by following formula:

Using Excel's function , the P-value for in an power-tailed t-test with 42 degrees of freedom can be computed as

Since P = 0.0053 < 0.01, we reject the null hypothesis in favor of the alternative hypothesis

Since the sample size is n = 43, degrees of freedom on the t-test statistic are n-1 = 43-1 = 42

This implies that

Since, the t distribution is symmetric about zero, so

Since , we reject the null hypothesis in favor of the alternative hypothesis .