Exercises 1 - 5

Exercise 1

0.9458

Exercise 2

0.9713

Exercise 3

0.1109

Exercise 4

589

Exercise 5

6.04, 6.22

Exercises 6 - 10

Exercise 6

71, 80

Exercise 7

21.9

Exercise 8

0.2307

Exercise 9

0.0753

Exercise 10

0.0181

Exercises 11 - 15

Exercise 11

1

Exercise 12

0

Exercise 13

3.8, 4

Exercise 14

16.3, 16.9

Exercise 15

Step 1: Top right

Step 2: 1.7

Exercises 16 - 18

Exercise 16

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

Exercise 17

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

Exercise 18

Assuming the previous study was exhaustive enough to be comfortable using 1.9 as a population sd:
1418

Exercises 19 - 21

Exercise 19

385

Exercise 20

## 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

Exercise 21

## 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