The average number of accidents at controlled intersections per year is 4.6. Is this average less for intersections with cameras installed? The 52 randomly observed intersections with cameras installed had an average of 4.2 accidents per year and the standard deviation was 1.07. What can be concluded at the αα = 0.01 level of significance?
H0: ? μ p ? ≠ > < =
H1: ? p μ ? ≠ = > <
Here we have to test that
,
Here population standard deviation is not given so we will use here t test.
Test statistic:
t = - 2.696 (Round to 3 decimal)
Test statistic = - 2.696
P value:
Test is one tailed (left tailed) test.
Degrees of freedom = n - 1 = 52- 1= 51
Level of significance = alpha = 0.01
P value from excel using command:
=T.DIST.RT(2.696,51)
= 0.004745
P value = 0.004745
Here P value < alpha
So we reject null hypothesis.
Conclusion: The data suggest that the population mean is significantly less than 4.6 at αα = 0.01, so there is statistically significant evidence to conclude that the population mean number of accidents per year at intersections with cameras installed is less than 4.6 accidents.
Interpretation of P value:
If the population mean number of accidents per year at intersections with cameras installed is 4.6 and if another 52 intersections with cameras installed are observed then there would be a 0.47450271% chance that the population mean number of accidents per year at intersections with cameras installed would be less than 4.6.
Interpretation of level of significance:
If the population population mean number of accidents per year at intersections with cameras installed is less than 4.6 and if another 52 intersections with cameras installed are observed then there would be a 1% 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 4.6.
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