Margin of Error for Proportions

Margin of error equals:

• Critical Value ∗ standard Error

• z*

• 1.96

• Standard Error

The Gallup Poll interviews 1600 people. Of these,18% say that they jog regularly. The news report adds: “The poll had a margin of error of plus or minus three percentage points at a 95% confidence level.”

You can safely conclude that

• 95% of all Gallup Poll samples like this one give answers within ±3% of the true population value.

• if Gallup took many samples, 95% of them would find that 18% of the people in the sample jog.

• the percent of the population who jog is certain to be between 15% and 21%.

• 95% of the population jog between 15% and 21% of the time.

• we can be 95% confident that the sample proportion is captured by the confidence interval.

A confidence interval for a difference in proportions is −0.077 to 0.013. What are the point estimate and the margin of error for this interval?

• –0.032, 0.045

• –0.032, 0.090

• –0.032, 0.180

• –0.045, 0.032

• –0.045, 0.090

Many television viewers express doubts about the validity of certain commercials. In an attempt to answer their critics, Timex Group USA wishes to estimate the true proportion p of all consumers who believe what is shown in Timex television commercials. What is the smallest number of consumers that Timex can survey to guarantee a margin of error of 0.05 or less at a 99% confidence level? Round up to the nearest whole number.

400 randomly selected adults were sampled. The proportion of people who like ice cream was found to be 82%. Find the Margin of Error with 95% confidence for this study. 

• 0.074

• 0.192

• 0.037

• 0.368

Complete the equation: 
point estimate +/- _____

• standard deviation

• margin of error

• critical value

• confidence level

A quality control inspector will measure the salt content (in milligrams) in a random sample of bags of potato chips from an hour of production. Which of the following would result in the smallest margin of error in estimating the percent of chips that are too salty?

• 90% confidence; n = 25 

• 95% confidence; n =25 

• 95% confidence; n =50 

• 90% confidence; n = 50 

• n=100 at any confidence level 

A quality control inspector will measure the salt content (in milligrams) in a random sample of bags of potato chips from an hour of production. Which of the following would result in the smallest margin of error in estimating the percent of chips that are too salty?

• 90% confidence; n = 25 

• 90% confidence; n = 50 

• 95% confidence; n =25 

• 95% confidence; n =50 

• n=100 at any confidence level 

A study found that in a sample of 44 subjects, 9 of agree that children under 6 shouldn’t be taken to nice restaurants. The 95% confidence interval is (0.082, 0.318). What is the margin of error?

• 0.236

• 0.118

• 0.2

• 0.095

A random sample of 692 adults revealed that 54% stream Netflix. If p hat = .54, what is the margin of error in this sample?