) Let's examine the levels of levels of sodium in the blood. 20 people yield the following results (in mEq/L): y = 136.95s =2.544%3D (a) Test Ho: µ = 140

using a = 0.001 (that's not a typo). (b) Figure out the p-value. To do this, take the t value that you calculated in (a) and use R: pt (absolute-value-of-your-t*, df, lower.tailFALSE)*2 Since it's a two sided test, you need to multiply by 2 at the end. We'll talk more about thisin lecture when we do one sided tests; for now just realize that without the “*2" at the endR gives you a one sided p-value. For example, if your t* = 4.65 and you have 67 degrees of freedom you would do: pt(4.65,67,lower.tailFALSE)*2 and you would get back 1.609352e-05 (c) Is the p-value smaller than a? (d) Why is this (c) important (see also part (a))? It is essential that you understand question (c)! (e) What is the smallest value of a for which you would reject the H,? Hint: this will not be a "standard"value of a. The correct answer here is a value that is not only small, but totally absurd). Another hint: think about the relationship of p-values to a. As mentioned in (d) it is very important thatyou understand the connection between a and p-values.