4. The following intervals were plausible population proportions for a given sample. Find the margin of error in each case.

a. From 0.35 to 0.65

b. From 0.72 to 0.78

c. From 0.84 to 0.95

d. From 0.47 to 0.57

Answer: a. 0.15 b. 0.03 c. 0.055 d. 0.05

Step-by-step explanation:

For plausible intervals of population proportions, the margin of error is basically half of the difference between upper limit and lower limit.

a. Interval = From 0.35 to 0.65

Upper limit = 0.65

Lower limit = 0.35

Difference = Upper limit - Lower limit

= 0.65-0.35=0.30

Margin of error = (Difference) : 2 = (0.30) : 2=0.15

b. Interval = From 0.72 to 0.78

Upper limit = 0.78

Lower limit = 0.72

Difference = 0.78-0.72 = 0.06

Margin of error = (0.06) : 2=0.03

c. Interval = From 0.84 to 0.95

Upper limit = 0.95

Lower limit = 0.84

Difference = 0.95-0.84 = 0.11

Margin of error = (0.11) : 2 = 0.055

d. Interval = From 0.47 to 0.57

Upper limit = 0.57

Lower limit = 0.47

Difference = 0.57-0.47=0.10

Margin of error = (0.10) : 2=0.05