Question

The police department in NYC is trying to determine if it is worth the cost to install a speed sensor and traffic camera on a highway near the city. They will install the speed sensor and traffic camera if convinced that more than 20% of cars are speeding. The police department selects a random sample of 100 cars on the highway, measures their speed, and finds that 28 of the 100 cars are speeding. A significance test is performed using the hypotheses.

Hoo: p=0 .20
Ha:p > 0.20
Where p is the true proportion of all cars on the highway that are speeding. The resulting p-value is 0.023. What conclusion would you make at the alpha level of 0.05 level?
A conclusion can be made that since the alpha level is less than the p-level, then we fail to reject the null hypothesis due p-value being 0.023 being greater than alpha level 0.05.

Answer 1

At a 5 percent significance level and with a p-value of 0.023, we reject the null hypothesis, concluding that more than 20% of cars are speeding.

Step-by-step explanation:

The question involves determining whether to reject the null hypothesis based on a p-value from a statistical test concerning the true proportion of cars that are speeding on a highway. Since the p-value of 0.023 is less than the alpha level of 0.05, we would reject the null hypothesis (H0: p = 0.20). At the 5 percent significance level, there is sufficient evidence to conclude that more than 20% of cars are speeding on the highway.