Find the indicated quantities – show all R code used to arrive at your answers.

  1. \(z_{0.04}=\)
qnorm(0.04)
## [1] -1.750686
  1. \(t_{0.92, 20}=\)
qt(.92, 20)
## [1] 1.459341
  1. \(P(t_4 \leq 0.10)=\)
pt(0.10, 4)
## [1] 0.5374221
  1. A random sample of 16 students revealed a mean score of 7.8 with a standard deviation of 1.15. Assuming the distribution of quiz scores follows a normal distribution, construct a 93% confidence interval for the true average quiz score.
library(PASWR2)
## Loading required package: lattice
## Loading required package: ggplot2
tsum.test(mean.x = 7.8, s.x = 1.15, n.x = 16, conf.level = 0.93)$conf
## [1] 7.239105 8.360895
## attr(,"conf.level")
## [1] 0.93

Class Notes: Thinking back to the confidence interval formula…

\(CI_{1-\alpha}(\mu) = \bar{X} \pm t_{1-\frac{\alpha}{2}, n-1}*\frac{S}{\sqrt{n}}\)

Given: \(\bar{X} = 78\)

Given: \(S = 1.15\)

\(0.93 = 1 - \alpha\)

\(\alpha = 0.07\)

\(t_{1-.035, 16-1} = t_{.965, 15}\)

\(t_{.965, 15} = 1.95\)