Respuesta :
Answer:
Henri’s margin of error = 0.104
Terence’s margin of error = 0.113
Step-by-step explanation:
It is given that Henri and Terence drew samples of size 50 from a mystery bag.
Formula for margin of error
[tex]M.E.=2\sqrt{\dfrac{p(1-p)}{n}}[/tex] ... (1)
where, p is the proportion.
Henri drew 42 red chips out of 50.
Proportion of getting red chip = [tex]\frac{42}{50}=0.84[/tex]
Substitute p=0.84 and n=50 in equation (1).
[tex]M.E.=2\sqrt{\dfrac{(0.84)(1-0.84)}{50}}[/tex]
[tex]M.E.=2\sqrt{\dfrac{(0.84)(0.16)}{50}}[/tex]
[tex]M.E.=0.10369[/tex]
[tex]M.E.\approx 0.104[/tex]
Henri’s margin of error is 0.104.
Terence drew 40 red chips.
Proportion of getting red chip = [tex]\frac{40}{50}=0.8[/tex]
Substitute p=0.8 and n=50 in equation (1).
[tex]M.E.=2\sqrt{\dfrac{(0.8)(1-0.8)}{50}}[/tex]
[tex]M.E.=2\sqrt{\dfrac{(0.8)(0.2)}{50}}[/tex]
[tex]M.E.=0.113137[/tex]
[tex]M.E.\approx 0.113[/tex]
Terence’s estimated margin of error is 0.113.
Answer:
The margins of error for Henri is 0.104.
The margins of error for Terence is 0.113.
Step-by-step explanation:
Consider the provided information.
Henri and Terence drew samples of size 50 from a mystery bag.
Henri drew 42 red chips,
[tex]\hat p=\frac{42}{50}=0.84[/tex]
The formula to calculate margins of error is: [tex]2\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
Substitute n = 50 and [tex]\hat p=0.84[/tex] in above formula.
Margin of error for Henri = [tex]2\sqrt{\frac{0.84(1-0.84)}{50}}[/tex]
Margin of error for Henri = [tex]2\sqrt{\frac{0.84(0.16)}{50}}[/tex]
Margin of error for Henri ≈ 0.104
Hence, the margins of error for Henri is 0.104.
Terence drew 40 red chips,
[tex]\hat p=\frac{40}{50}=0.84[/tex]
The formula to calculate margins of error is: [tex]2\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
Substitute n = 50 and [tex]\hat p=0.80[/tex] in above formula.
Margin of error for Terence = [tex]2\sqrt{\frac{0.80(1-0.80)}{50}}[/tex]
Margin of error for Terence = [tex]2\sqrt{\frac{0.8(0.2)}{50}}[/tex]
Margin of error for Terence ≈ 0.113
Hence, the margins of error for Terence is 0.113.
