The British Medical Journal published an article titled, "Is...

The British Medical Journal published an article titled, "Is Friday the 13 th Bad for Your Health?" Researchers in Britain examined how Friday the 13 th affects human behavior. One question was whether people tend to stay at home more on Friday the 13 th. The data below are the number of cars passing Junctions 9 and 10 on the M25 motorway for consecutive Fridays (the 6 th and 13 th ) for five different periods. $$\begin{array}{|l|l|c|c|}\hline \text { Year } & \multicolumn{1}{|c|} {\text { Month }} & \text { 6th } & \multicolumn{1}{|c|} {13 \text { th }} \\ \hline 1990 & \text { July } & 134,012 & 132,908 \\ 1991 & \text { September } & 133,732 & 131,843 \\ 1991 & \text { December } & 121,139 & 118,723 \\ 1992 & \text { March } & 124,631 & 120,249 \\ 1992 & \text { November } & 117,584 & 117,263 \\ \hline\end{array}$$ a) Which of the tests is appropriate for these data? Explain. b) Using the test you selected, state your conclusion. c) Are the assumptions and conditions for inference met?

The British Medical Journal published an article titled, "Is Friday the 13 th Bad for Your Health?" Researchers in Britain examined how Friday the 13 th affects human behavior. One question was whether people tend to stay at home more on Friday the 13 th. The data below are the number of cars passing Junctions 9 and 10 on the M25 motorway for consecutive Fridays (the 6 th and 13 th ) for five different periods.
$$\begin{array}{|l|l|c|c|}\hline \text { Year } & \multicolumn{1}{|c|} {\text { Month }} & \text { 6th } & \multicolumn{1}{|c|} {13 \text { th }} \\
\hline 1990 & \text { July } & 134,012 & 132,908 \\
1991 & \text { September } & 133,732 & 131,843 \\
1991 & \text { December } & 121,139 & 118,723 \\
1992 & \text { March } & 124,631 & 120,249 \\
1992 & \text { November } & 117,584 & 117,263 \\
\hline\end{array}$$
a) Which of the tests is appropriate for these data? Explain.
b) Using the test you selected, state your conclusion.
c) Are the assumptions and conditions for inference met?

Key Concepts

Hypothesis Testing

Hypothesis testing is a framework in which an initial assumption (the null hypothesis) is tested against an alternative hypothesis to determine if there is a statistically significant effect. In the context of paired data, the null hypothesis typically states that there is no difference between the paired observations, while the alternative hypothesis claims that a difference exists, guiding the interpretation of the experimental results.

Assumptions for Inference

Statistical tests like the paired t-test require certain assumptions to be met for valid inference. These include the assumption that the differences between the paired observations are approximately normally distributed, that the pairs are independent of each other, and that the data are randomly sampled from the population. Meeting these conditions is essential to ensure the reliability and accuracy of the test results.

Paired T-Test

A paired t-test is a statistical method used to compare the means of two related groups. It is particularly appropriate when the data consist of matched pairs or repeated measurements of the same subjects under different conditions, as it accounts for the dependency between the paired observations and reduces variability due to individual differences.

Matched Pairs Design

A matched pairs design involves collecting data in pairs where each pair consists of observations from the same unit or closely related units under different conditions. This design is especially useful when comparing changes or differences in the same subjects over time or under different settings, ensuring that extraneous variability is minimized.

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