Confidence Intervals Homework

Solve these problems, then check your answers against the given solutions.

Solutions to Exercises

Solution to Exercise 1

i. 71

ii. 3
iii. 2.8

iv. 48

v. 47

$N (71, \dfrac{3}{\sqrt{48}})$

i. CI: (70.15,71.85)

iii. EB = 0.85

Solution to Exercise 2

i. 8629

ii. 6944
iii. 35

iv. 34

C. t₃₄

i. CI: (6243, 11,014)

iii. EB = 2385

e. It will become smaller

Solution to Exercise 3

i. 8

ii. 4

iii. 81

iv. 80

c. t₈₀

i. CI: (7.12, 8.88)

iii. EB = 0.88

Solution to Exercise 4

i. 2

ii. 0.1

iii. 0.12

iv. 16

v. 15

b. the weight of 1 small bag of candies
c. the average weight of 16 small bags of candies
d.

$N (2, \dfrac{0.1}{\sqrt{16}})$

i. CI: (1.96, 2.04)

iii. EB = 0.04

i. CI: (1.94, 2.06)

iii. EB = 0.06

Solution to Exercise 5

i. 6

ii. 3

iii. 14

iv. 13

b. the time for a child to remove his training wheels
c. the average time for 14 children to remove their training wheels.
d. t₁₃

i. CI: (3.58, 8.42)

iii. EB = 2.42

Solution to Exercise 6

i. 320

ii . 400

iii. 0.80

$N (0.80, \sqrt{\dfrac{(0.80)(0.20)}{400}})$

i. CI: (0.76, 0.84)

iii. EB = 0.04

Solution to Exercise 7

$N (0.86, \sqrt{\dfrac{(0.86)(0.14)}{323}})$

i. CI: (0.59, 0.63)

iii. EB = 0.02

Solution to Exercise 8

i. 7.9

ii. 2.5

iii. 2.8

iv. 20

v. 19

$N (7.9, \dfrac{2.5}{\sqrt{20}})$

i. CI: (6.98, 8.82)

iii. EB:0.92

Solution to Exercise 9

a. t₈₃
b. average cost of 84 used cars

i. CI: (5740.10, 7109.90)

iii. EB = 684.90

BUS204: Business Statistics