Let's examine the levels of levels of sodium in the blood. 20 people yield the following results (in mEq/L): ̄y = 133.95 s = 2.544 (a) Test H0: μ = 137 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))? (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)
3)
Let's examine the levels of levels of sodium in the blood. 20 people yield the following results (in mEq/L):
̄y = 133.95 s = 2.544
(a) Test H0: μ = 137 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))?
(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)
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
