$\newcommand{\E}{\mathbb{E}}$

For today’s code challenge, we’ll use the data mtcars which comes loaded with R.

Calculate the p-values for testing the following hypotheses.

1. $$\E[mpg] = 20$$

2. $$\E[cyl] = 5$$

3. $$\E[disp] = 150$$

4. $$\E[hp] = 150$$

5. $$\E[drat] = 4$$

6. $$\E[wt] = 3$$

7. $$\E[qsec] = 10$$

8. $$\E[vs] = 0.5$$

9. $$\E[am] = 0.5$$

10. $$\E[gear] = 4$$

11. $$\E[carb] = 4$$

Rules:

• You cannot load any external packages, and you cannot use any kind of pvalue function (if there is one…)

• The maximum amount of code that you can send me is 10 lines

To win

• You must email me your code brantly.callaway@uga.edu

• I’ll run exactly the code that you send me, and if your code gets all 11 p-values correct, then you win.

Solution below…

n <- nrow(mtcars)
h0 <- c(20, 5, 150, 150, 4, 3, 10, 0.5, 0.5, 4, 4)
p <- c()
for (i in 1:ncol(mtcars)) {
t <- sqrt(n)*(mean(mtcars[,i])-h0[i])/sqrt(var(mtcars[,i]))
p[i] <- 2*pnorm(-abs(t))
}
round(p,6)
##  [1] 0.932214 0.000169 0.000229 0.784622 0.000020 0.209113 0.000000 0.483008
##  [9] 0.287870 0.016576 0.000032