Question

A safety officer wants to prove that the average speed of cars driven by a school is lessthan 25 mph. Suppose that a random sample of 14 cars shows an average speed of 24.0 mph, with a sample standard deviation of 2.2 mph. Assume that the speeds of cars are normally distributed. What are the appropriate null and alternative hypotheses? Testing at significance level of α=5% if the p-value = 0.057, what is an appropriate conclusion?

Answer 1

Null hypothesis $H_0:\;\mu=25.$

Alternative hypothesis $H_a:\mu<25.$

Since the P-value is greater than 0.05, fail to reject the null hypothesis at $\alpha=0.05.$

There is no sufficient evidence to conclude that the average speed of cars driven by a school is less than 25 mph.