Margin of Error

The sample size of poll is 107 people. What is the approximate margin of error.

• 10%

• 3.1%

• 2.38%

• 1%

Tags

CCSS.HSS.IC.B.4

As a data scientist you have been asked to compare the difference of two percentages within the same survey. Which margin of error rule would you use?

• $\frac{1}{\sqrt{n}}$

• $2\times\frac{1}{\sqrt{n}}$

• $1.5\times average\ MoE$

• $\frac{2}{\sqrt{n}}$

• $\sqrt{n}$

To cut the margin of error in half, the sample size would have to increase by ______________.

• 100

• 2 times

• 3.1%

• 4 times

A survey of 400 people is done, what is the approximate margin of error.

• 5%

• 3.1%

• 20%

• 10%

Tags

CCSS.HSS.IC.B.4

From a survey of 400 people (MoE $\approx$ 5%), a claim is made that  "over 60% of old people wear dentures."  
Under what circumstances could this claim be made.

• If the proportion of old people wearing dentures is greater than 60%.

• If the proportion of old people wearing dentures is 61%.

• If the proportion of old people wearing dentures is more than 65%.

• If the proportion of old people wearing dentures is 65%.

Of 900 surveyed New Zealanders, the proportion of Labour supporters is 45% and for National it is 38% (undecideds are ignored). The difference between these two percentages is 7 perc pts. Can the claim that more NZers support Labour be made?

• Yes, because the Confidence Interval is [0.4 perc pts , 13.6 perc pts] and is greater than 0 perc pts. This means that support for labour could be as low as 0.4 perc pts more than National to as much as 13.6 perc pts more than National.

• Yes

• Yes, because the Confidence Interval is [3.7 perc pts , 10.3 perc pts] and it is greater than 0 perc pts.This means that support for labour could be as low as 3.7 perc pts more than National to as much as 10.3 perc pts more than National.

• No, the sample of New Zealanders is too small.

In a single survey, 150 men and 350 women were interviewed about their movie viewing habits. Which is the most appropriate Margin of error rule to use for comparing the two groups?

•  $\frac{1}{\sqrt{n}}$  because this is the rule of thumb for calculating margins of error.

•  $\frac{2}{\sqrt{n}}$  because this is used for comparing proprotions within the same survey.

•  $1.5\times average\ MoE$  because males and females are statistically considered two independent groups even if they are in the same survey.

A survey (n=500) was carried out to identify male and female movie habits. They interviewed 150 men and 350 women. 53% of men said they preferred action movies and 49% of women said they preferred action movies.

Can the claim "More men liked action movies" be made ?

• Yes, men who prefer action movies are 4 perc. pts greater than females.

• Yes, because the CI = [ 0.9 perc pts , 7.1 perc pts ]. The percentage of men could be 0.9 perc pts higher to as much as 7.1 perc pts higher.

• No, because the CI = [ -4.9 perc pts , 12.9 perc pts ]. The percentage of men could be 4.9 perc pts lower, possibly equal or as much as 12.9 perc pts higher.

• No, because the CI = [ -9.7 perc pts , 17.7 perc pts ]. The percentage of men could be 9.7 perc pts lower, possibly equal or as much as 17.7 perc pts higher.