Explain why we use the term do not reject hypothesis

Question

Part (a)

Suppose that someone claims that adult koalas eat an average of 392 grams of eucalyptus leaves per day. Using information from a sample of 50 koalas (sample mean = 395 grams, sample standard deviation = 53 grams), carry out a hypothesis test (via the 6-step procedure or using the p-value) with a level of significance a = 0.01 to test H₀: µ = 392 and show your work.

Part (b)

Does your result in part (a) prove that the population mean is 392 grams? Explain your answer.

Part (c)

Suppose that someone claims that adult koalas eat an average of 398 grams of eucalyptus leaves per day. Using information from a sample of 50 koalas (sample mean = 395 grams, sample standard deviation = 53 grams), carry out a hypothesis test (via the 6-step procedure or using the p-value) with a level of significance a = 0.01 to test H₀: µ = 398 and show your work.

Part (d)

Does your result in part (c) prove that the population mean is 398 grams? Explain your answer.

Part (e)

Use your results from above, to explain why we use the term "do not reject H₀" and not "accept H₀". (Hint: You may also wish to go back to your answers to parts (b) and (d) to make sure that they are consistent with your answer to this part.)