Let's examine the levels of levels of sodium in the blood. 20 people yield the following results (in mEq/L): ̄y = 136.95 s = 2.544 (a) Test H0: μ = 140 using α = 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.tail = FALSE)*2 Since it's a two sided test, you need to multiply by 2 at the end. We'll talk more about this in lecture when we do one sided tests; for now just realize that without the “*2” at the end R gives you a one
3) Let's examine the levels of levels of sodium in the blood. 20 people yield the following results (in mEq/L): ̄y = 136.95 s = 2.544
(a) Test H0: μ = 140 using α = 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.tail = FALSE)*2
Since it's a two sided test, you need to multiply by 2 at the end. We'll talk more about this in lecture when we do one sided tests; for now just realize that without the “*2” at the end R 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.tail = FALSE)*2
and you would get back 1.609352e-05 (c) Is the p-value smaller than α?
(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 α for which you would reject the H0? Hint: this will not be a “standard” value of α. 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 α. As mentioned in (d) it is very important that you understand the connection between α and p-values.
(e) For which of the following values of α would you reject? Why (see (c))?
i) .10 ii) .05 iii) .01 iv) .001 v) .00000001
(note that no one in their right mind would actually use α = .00000001)
Please only answer the questions in bold. Thank you !
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