The data provides some evidence to support the alternative hypothesis that the proportion of drivers under the influence of alcohol has decreased during the pandemic.
Null Hypothesis: The proportion of drivers under the influence of alcohol on Saturday nights is 0.88, as suggested by law enforcement research.
Alternative Hypothesis: The proportion of drivers under the influence of alcohol on Saturday nights has decreased during the pandemic, as suggested by Northeastern researchers.
Probability of observing exactly x drivers under the influence:
p = 0.88 (null hypothesis)
q = 1 - p = 0.12
n = 66
x = 53
Therefore, the probability of observing exactly 53 drivers under the influence is:
P(X = 53) = ⁶⁶C₅₃ * 0.88⁵³ * 0.12¹²
≈ 0.0000398
We can use a statistical software or online calculator to compute the CDF. In this case:
P(X ≥ 53) ≈ 0.023
The probability of observing at least 53 drivers under the influence of alcohol in a sample of 66, under the assumption that the true proportion of drivers under the influence is 0.88, is approximately 0.023. This is a relatively low probability, suggesting that the observed data is unlikely to have occurred by chance if the null hypothesis is true.
Therefore, the data provides some evidence to support the alternative hypothesis that the proportion of drivers under the influence of alcohol has decreased during the pandemic.