Friday the 13th, Part II

Friday the 13th, Part II#

In the early 1990’s, researchers in the UK collected data on traffic flow, number of shoppers, and traffic accident related emergency room admissions on Friday the \(13^{th}\) and the previous Friday, Friday the \(6^{th}\). The distributions of data on traffic accident related emergency room admissions from Friday the \(6^{th}\) and Friday the \(13^{th}\) are shown below for six such paired dates along with summary statistics. You may assume that conditions for inference are met.

Part 1#

What are the hypotheses to evaluate if there is a difference between the average numbers of traffic accident related emergency room admissions between Friday the \(6^{th}\) and Friday the \(13^{th}\)?

Answer Section#

  • \(H_0 : μ_{6^{th}} = μ_{13^{th}}\). \(H_A : μ_{6^{th}} > μ_{13^{th}}\)

  • \(H_0 : μ_{diff} = 0\). \(H_A : μ_{diff} ≠ 0\)

  • \(H_0 : μ_{diff} > 0\). \(H_A : μ_{diff} ≤ 0\)

  • \(H_0 : μ_{6^{th}} = μ_{13^{th}}\). \(H_A : μ_{6^{th}} = μ_{13^{th}}\)

Part 2#

Calculate the test statistic.

Answer Section#

Please enter a numeric value in.

Part 3#

Calculate the p-value.

Answer Section#

Please enter a numeric value in.

Part 4#

What is the conclusion of the hypothesis test?

Answer Section#

  • The data suggest that there is no significant difference in the average number of traffic accident-related emergency room admissions between Friday the \(6^{th}\) and Friday the \(13^{th}\).

  • The data provide strong evidence that the average number of traffic accident related emergency room admissions are different between Friday the \(6^{th}\) and Friday the \(13^{th}\).

  • The results confirm with \(100\)% certainty that there are more accidents on Friday the \(6^{th}\) compared to Friday the \(13^{th}\).

  • The data indicate that the number of accidents on Friday the \(13^{th}\) is significantly higher, proving the superstition about the day being unlucky.

Part 5#

Calculate the lower bound of a \(95\)% confidence interval for the difference between the average numbers of traffic accident related emergency room admissions between Friday the \(6^{th}\) and Friday the \(13^{th}\).

Answer Section#

Please enter a numeric value in.

Part 6#

Calculate the upper bound bound of a \(95\)% confidence interval for the difference between the average numbers of traffic accident related emergency room admissions between Friday the \(6^{th}\) and Friday the \(13^{th}\).

Answer Section#

Please enter a numeric value in.

Part 7#

The conclusion of the original study states, “Friday \(13^{th}\) is unlucky for some. The risk of hospital admission as a result of a transport accident may be increased by as much as \(52\)%. Staying at home is recommended.” Do you agree with this statement? Explain your reasoning.

Answer Section#

  • Observational studies do not imply causation, and the difference observed does not necessarily mean increased risk for a responsible adult going out on Friday the \(13^{th}\).

  • The study conclusively proves that Friday the \(13^{th}\) is an unlucky day with a consistent \(52\)% increase in the risk of transport accident-related hospital admissions.

Attribution#

Problem is from the OpenIntro Statistics textbook, licensed under the CC-BY 4.0 license.
Image representing the Creative Commons 4.0 BY license.