Question

County despite traffic lights. The Traffic Department claims that a modification in the type of light will reduce these accidents. The county commissioners have agreed to a proposed experiment Eight intersections were chosen at random, and the lights at those intersections were modified. The numbers of minor accidents during a six-month period before and after the modifications were: Number of Accidents A B C DEF G H Before modification After modification 3 7 7 4 6 8 2 Click here for the Excel Data File At the 01 significance level, is it reasonable to conclude that the modification reduced the number of traffic accidents? Hint For the calculations, assume theAfter modification as the first sample Reject Hoif s 1895 (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.) The test statistic is [242 O (Negative value should be indicated by a minus sign Round your answer to 2 decimal places.) Decision: Donotreject] Ho : μ σ=0

Answer 1

The following table is obtained: Difference Sample 1 - Sample2 Sample 1 Sample 2 2 6 -3 10 -8 Average 4.625 7.125 -2.5 St. Dev 2.825 2.031 2.928 From the sample data, it is found that the corresponding sample means are: X1 4.625

b = 7.125 Also, the provided sample standard deviations are 812.825 89 2.031 and the samole size is nts 8. For the score diferences we have D =-2.5 SD 2.928 (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested This corresponds to a left-tailed test, for which a t-test for two paired samples be used. 0.01, and the degrees of freedom Based on the information provided, the significance level is are df 7

Hence, it is found that the critical value for this left-tailed test is te2.998, for a 0.01 and df- The rejection region for this left-tailed test is R {t : t <-2.998) (3) Test Statistics The t-statistic is computed as shown in the following formula 2.5 SD/Vn 2.928/v82415 (4) Decision about the null hypothesis 2. i 5 > t 93郑8, ii is then cx" cluckx thai the null hyp Sin(x: it is obsorvex1 iliat i not rejected. hasis is Using the P-value approach: The p-value is p 0.0232, and since p 0.02322 0.01, it is concluded that the null hypothesis is not rejected. It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ| is less than μ2, at the 0.01 significance level. Confidence Interval The 99% confidence interval is-6.122 < μD < 1.122.