Carrying Out Test for Population Mean Practice Test

An online retailer wants to check whether the mean delivery time for a certain shipping option is 2 days. A random sample of 100 deliveries is selected, and a one-sample $t$ test is performed with $H_0:\mu=2$ versus $H_a:\mu\ne 2$ at $\alpha=0.05$. The p-value is 0.58. What conclusion is appropriate?

A hospital states that the mean length of stay for patients undergoing a certain procedure is $\mu=3.5$ days. A researcher suspects the mean length of stay has decreased with a new protocol. A random sample of 22 patients is collected, and a one-sample $t$ test is conducted with $H_0:\mu=3.5$ versus $H_a:\mu<3.5$ at $\alpha=0.05$. The p-value is 0.049. What conclusion is appropriate?