Question

CNN Money reports that the average cost of a speeding ticket, including court costs, was $150 in 2019. A local police department claims that this amount has increased. To test their claim, they collect data from 160 drivers who have been fined in the last year and find that they paid an average of $154 per ticket with a standard deviation of $17.54. Is there evidence to support the police department’s claim at the 0.01 level of significance?

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 150
Alternative Hypothesis, Ha: μ > 150

Rejection Region
This is right tailed test, for α = 0.01 and df = 159
Critical value of t is 2.35.
Hence reject H0 if t > 2.35

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (154 - 150)/(17.54/sqrt(160))
t = 2.885

P-value Approach
P-value = 0.0022
As P-value < 0.01, reject the null hypothesis.

Conclusion
There is sufficient evidence to conclude that this amount has increased