Question

The average number of accidents at controlled intersections per year is 4.1. Is this average more for intersections with cameras installed? The 43 randomly observed intersections with cameras installed had an average of 4.3 accidents per year and the standard deviation was 0.63. What can be concluded at the αα = 0.05 level of significance?

1. For this study, we should use Select an answer z-test for a population proportion t-test for a population mean
2. The null and alternative hypotheses would be:

H0:H0:  ? μ p  ? > = ≠ <       

H1:H1:  ? μ p  ? < = > ≠    

3. The test statistic ? z t  =  (please show your answer to 3 decimal places.)
4. The p-value =  (Please show your answer to 4 decimal places.)
5. The p-value is ? > ≤  αα
6. Based on this, we should Select an answer accept reject fail to reject  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest that the population mean is not significantly more than 4.1 at αα = 0.05, so there is statistically insignificant evidence to conclude that the population mean number of accidents per year at intersections with cameras installed is more than 4.1 accidents.
   • The data suggest that the sample mean is not significantly more than 4.1 at αα = 0.05, so there is statistically insignificant evidence to conclude that the sample mean number of accidents per year at intersections with cameras installed is more than 4.3 accidents.
   • The data suggest that the populaton mean is significantly more than 4.1 at αα = 0.05, so there is statistically significant evidence to conclude that the population mean number of accidents per year at intersections with cameras installed is more than 4.1 accidents.
8. Interpret the p-value in the context of the study.
   • If the population mean number of accidents per year at intersections with cameras installed is 4.1 and if another 43 intersections with cameras installed are observed then there would be a 2.17496463% chance that the population mean number of accidents per year at intersections with cameras installed would be greater than 4.1.
   • If the population mean number of accidents per year at intersections with cameras installed is 4.1 and if another 43 intersections with cameras installed are observed then there would be a 2.17496463% chance that the sample mean for these 43 intersections with cameras installed would be greater than 4.3.
   • There is a 2.17496463% chance that the population mean number of accidents per year at intersections with cameras installed is greater than 4.1 .
   • There is a 2.17496463% chance of a Type I error.
9. Interpret the level of significance in the context of the study.
   • There is a 5% chance that the population mean number of accidents per year at intersections with cameras installed is more than 4.1.
   • If the population mean number of accidents per year at intersections with cameras installed is 4.1 and if another 43 intersections with cameras installed are observed then there would be a 5% chance that we would end up falsely concluding that the population mean number of accidents per year at intersections with cameras installed is more than 4.1.
   • If the population population mean number of accidents per year at intersections with cameras installed is more than 4.1 and if another 43 intersections with cameras installed are observed then there would be a 5% chance that we would end up falsely concluding that the population mean number of accidents per year at intersections with cameras installed is equal to 4.1.
   • There is a 5% chance that you will get in a car accident, so please wear a seat belt.

Answer 1

x̅ = 4.3, s = 0.63, n = 43

a) Test used : t-test for a population mean

b) The null and alternative hypotheses would be:

Ho : µ ≤ 4.1

H1 : µ > 4.1

c) Test statistic:

t = (x̅- µ)/(s/√n) = (4.3 - 4.1)/(0.63/√43) = 2.082

d) p-value = T.DIST.RT(2.0817, 42) = 0.0217

e) The p-value is ≤ α.

f) Based on this, we should reject the null hypothesis.

g) Thus, the final conclusion is that :

The data suggest that the population mean is significantly more than 4.1 at α = 0.05, so there is statistically significant evidence to conclude that the population mean number of accidents per year at intersections with cameras installed is more than 4.1 accidents.

h) Interpret the p-value in the context of the study.

If the population mean number of accidents per year at intersections with cameras installed is 4.1 and if another 43 intersections with cameras installed are observed then there would be a 2.17496463% chance that the population mean number of accidents per year at intersections with cameras installed would be greater than 4.1.

i) Interpret the level of significance in the context of the study.

There is a 5% chance that the population mean number of accidents per year at intersections with cameras installed is more than 4.1.