Peter has been bench pressing 825.0 Ibs. for many ( so = 825. 0). A fitness guru sells him a workout machine he claims will increase the amount Peter can bench press. A proper and appropriate hypothesis test was conducted using 14 random bench presses to see if there was any statistically significant improvement. It was found that the sample mean was 826.4. and the sample standard deviation was 10.35. Based on these numbers, it was correctly determined that at the alpha 0.05 level, p = 0.307 and power = 0.13.

What does the p-value tell you?

What type of error could you have made?

What does power mean in context?

Explain two ways to increase the power of this test.

If the sample mean were 836.4, what would the power increase, decrease, or stay the same?

What is the probability that you have made a Type I error?

What is the probability that you have made a Type II error?