Exercise

Testing a claim

Suppose that after observing the data, Rebekah's beliefs about the proportion of college women P who think they are overweight is described by a beta curve with shape parameters 24.13 and 7.67.

Suppose a researcher makes the claim that among all college women, 90 percent believe they are overweight. How can you test this claim?

In other words, you are interested in the plausibility of the hypothesis:

$$ H: P > 0.90 $$

You can use the pbeta() function to compute the probability of this hypothesis from the \(beta(24.13, 7.67)\) curve.

Then you can use the beta_area() function to visualize this area:

ab <- c(24.13, 7.67)
1 - pbeta(0.90, ab[1], ab[2])
beta_area(0.90, 1, ab)

Instructions

100 XP

Suppose another researcher believes that the proportion P is smaller than 0.70. Harry wants to check this claim; Harry's beliefs about P are described by a \(beta(19, 7)\) curve.

  • Store the shape parameters of Harry's beta curve in a vector called ab.
  • Use the function pbeta() to compute the probability P is smaller than 0.70.
  • Use the beta_area() function to visualize this probability.