A team of research doctors designed a new knee surgery technique utilizing much smaller incisions than the standard method. They believe recovery times are shorter when the new method is used. Under the old method, the average recovery time for full use of the knee is ₁ = 4.5 months. A random sample of 39 surgeries using the new method showed the average recovery time to be ₂ = 3.7 months, with sample standard deviation of 1.5 months. The P-value for the test is 0.0010. The research team states that the results are statistically significant at the 1% level of significance.

Describe the hypotheses. Null hypothesis: the average recovery times are the same; Alternate hypothesis: the average recovery time for the new method is not the same as the average recovery time for the old methodNull hypothesis: the average recovery times are the same; Alternate hypothesis: the average recovery time for the new method is less than the average recovery time for the old method Null hypothesis: the average recovery times are the same; Alternate hypothesis: the average recovery time for the new method is greater than the average recovery time for the old methodNull hypothesis: the average recovery time for the new method is less than the average recovery time for the old method; Alternate hypothesis: the average recovery times are the same

What does the P-value mean? It is the probability that a sample could be gathered from the population with the given characteristics.It is the probability that the population could have a sample like this again. It is the probability that the sample has that mean.It is the probability that the population actually has that mean.

What is the meaning of a Type II error?

Accept the hypothesis that the average recovery times are the same when in fact this is true.Accept the hypothesis that the average recovery times are the same when in fact this is false. Reject the hypothesis that the average recovery times are different when in fact this is true.Reject the hypothesis that the average recovery times are different when in fact th

What does it mean to be statistically significant at the 1% level of significance?