Learning Targets

• Use simulation to approximate the margin of error for a sample proportion and interpret the margin of error.

• Use simulation to approximate the margin of error for a sample mean and interpret the margin of error.

Do you expect that this mean of 5 is the same as the true population mean?

No, because of sampling variability we know that if we continue to sample students in groups of 25 we will get different means. Some will be above and some will be below our sample mean of 5.

One Quantitative Variable

• Enter the data and begin analysis.

• Scroll down to Perform Inference and choose Simulate sample mean.

Draw and label

• The mean (5.051)

• One SD (0.292) above and below

• Two SD (0.584) above and below

Interval that includes all the data two SD above and below the mean.

• mean: 5.051 and SD: 0.292

• 5.051 + 2(0.292) = 5.635

• 5.051 - 2(0.292) = 4.467

• Confidence Interval: (4.467, 5.635)

Margin of Error

We multiply the standard deviation by 2 in order to get the margin of error. The reason is because a majority of our estimates will be within 2 standard deviations away from the mean (should be around 95%). 

In this example, the margin of error = 2(0.292) = 0.584.

One Categorical Variable

• Scroll down to Perform Inference

Margin of Error

• = 2(Standard Deviation)

• = 2(0.064)

• = 0.128

• We expect the true proportion of students who text during class to be at most 0.128 from the estimate of 0.639

Is a claim that 75% of people can roll their tongue plausible?

Yes, the true proportion can be as low as 0.701 - 0.096 = 0.605 or as high as 0.701 + 0.096 = 0.797 The confidence interval is (0.605, 0.797) and .75 falls within that interval. So 75% is plausible.