0.9458
0.9713
0.1109
589
6.04, 6.22
71, 80
21.9
0.2307
0.0753
0.0181
1
0
3.8, 4
16.3, 16.9
Step 1: Top right
Step 2: 1.7
values <- c(383.6, 347.1, 371.9, 347.6, 325.8, 337)
n <- length(values)
df <- n - 1
ci <- 0.90
alpha <- (1-ci)/2
## Step 1
x_bar <- round(mean(values), 2)
x_bar
## [1] 352.17
## Step 2
s <- round(sd(values), 2)
s
## [1] 21.68
## Step 3
t_score <- round(qt(alpha, df=df, lower.tail = F), 3)
t_score
## [1] 2.015
## Step 4
round(x_bar - t_score * (s / sqrt(n)), 2)
## [1] 334.34
round(x_bar + t_score * (s / sqrt(n)), 2)
## [1] 370
x_bar <- 46.4
s <- 2.45
n <- 16
df <- n - 1
ci <- 0.80
alpha <- (1-ci)/2
## Step 1
t_score <- round(qt(alpha, df=df, lower.tail = F), 3)
t_score
## [1] 1.341
## Step 2
round(x_bar - t_score * (s / sqrt(n)), 2)
## [1] 45.58
round(x_bar + t_score * (s / sqrt(n)), 2)
## [1] 47.22
Assuming the previous study was exhaustive enough to be comfortable using 1.9 as a population sd:
1418
385
## Step 1
x <- 1734
n <- 2089
p <- round(1-x/n, 3)
p
## [1] 0.17
## Step 2
round(p - qnorm(0.99)*sqrt(p*(1-p)/n), 3)
## [1] 0.151
round(p + qnorm(0.99)*sqrt(p*(1-p)/n), 3)
## [1] 0.189
## Step 1
x <- 156
n <- 474
p <- round(x/n, 3)
p
## [1] 0.329
## Step 2
round(p - qnorm(0.975)*sqrt(p*(1-p)/n), 3)
## [1] 0.287
round(p + qnorm(0.975)*sqrt(p*(1-p)/n), 3)
## [1] 0.371